Understanding Linear Algebra 649HGZKE96

URI	`m2://res/649HGZKE96`
Kind	textbook
Creators	David Austin
Date	2026-09-18
MSC	15-01
Scope	in

Expressions

e1: edition

Language	en
Date	2026-09-18

Contents

chapter 1: Systems of equations
section 1.1: What can we expect
subsection 1.1.1: Some simple examples
subsection 1.1.2: Systems of linear equations
subsection 1.1.3: Summary
section 1.2: Finding solutions to linear systems
subsection 1.2.1: Gaussian elimination
subsection 1.2.2: Augmented matrices
subsection 1.2.3: Reduced row echelon form
subsection 1.2.4: Summary
section 1.3: Computation with Sage
subsection 1.3.1: Introduction to Sage
subsection 1.3.2: Sage and matrices
subsection 1.3.3: Computational effort
subsection 1.3.4: Summary
section 1.4: Pivots and their influence on solution spaces
subsection 1.4.1: Introduction
subsection 1.4.2: The existence of solutions
subsection 1.4.3: The uniqueness of solutions
subsection 1.4.4: Summary
chapter 2: Vectors, matrices, and linear combinations
section 2.1: Vectors and linear combinations
subsection 2.1.1: Vectors
subsection 2.1.2: Linear combinations
subsection 2.1.3: Summary
section 2.2: Matrix multiplication and linear combinations
subsection 2.2.1: Scalar multiplication and addition of matrices
subsection 2.2.2: Matrix-vector multiplication and linear combinations
subsection 2.2.3: Matrix-vector multiplication and linear systems
subsection 2.2.4: Matrix-matrix products
subsection 2.2.5: Summary
section 2.3: The span of a set of vectors
subsection 2.3.1: Introduction
subsection 2.3.2: The span of a set of vectors
subsection 2.3.3: Pivot positions and span
subsection 2.3.4: Summary
section 2.4: Linear independence
subsection 2.4.1: Introduction
subsection 2.4.2: Linear dependence
subsection 2.4.3: How to recognize linear dependence
subsection 2.4.4: Homogeneous equations
subsection 2.4.5: Summary
section 2.5: Matrix transformations
subsection 2.5.1: Introduction
subsection 2.5.2: Matrix transformations
subsection 2.5.3: Composing matrix transformations
subsection 2.5.4: Discrete Dynamical Systems
subsection 2.5.5: Summary
section 2.6: The geometry of matrix transformations
subsection 2.6.1: Introduction
subsection 2.6.2: The geometry of $2\times2$ matrix transformations
subsection 2.6.3: Matrix transformations and computer animation
subsection 2.6.4: Summary
chapter 3: Invertibility, bases, and coordinate systems
section 3.1: Invertibility
subsection 3.1.1: Introduction
subsection 3.1.2: Invertible matrices
subsection 3.1.3: Solving equations with an inverse
subsection 3.1.4: Triangular matrices and Gaussian elimination
subsection 3.1.5: Summary
section 3.2: Bases and coordinate systems
subsection 3.2.1: Introduction
subsection 3.2.2: Bases
subsection 3.2.3: Coordinate systems
subsection 3.2.4: Examples of bases
subsection 3.2.5: Summary
section 3.3: Image compression
subsection 3.3.1: Introduction
subsection 3.3.2: Color models
subsection 3.3.3: The JPEG compression algorithm
subsection 3.3.4: Summary
section 3.4: Determinants
subsection 3.4.1: Introduction
subsection 3.4.2: Determinants of $2\times2$ matrices
subsection 3.4.3: Determinants and invertibility
subsection 3.4.4: Cofactor expansions
subsection 3.4.5: Summary
section 3.5: Subspaces
subsection 3.5.1: Introduction
subsection 3.5.2: Subspaces
subsection 3.5.3: The column space of $A$
subsection 3.5.4: The null space of $A$
subsection 3.5.5: Summary
chapter 4: Eigenvalues and eigenvectors
section 4.1: An introduction to eigenvalues and eigenvectors
subsection 4.1.1: Introduction
subsection 4.1.2: A few examples
subsection 4.1.3: The usefulness of eigenvalues and eigenvectors
subsection 4.1.4: Summary
section 4.2: Finding eigenvalues and eigenvectors
subsection 4.2.1: Introduction
subsection 4.2.2: The characteristic polynomial
subsection 4.2.3: Finding eigenvectors
subsection 4.2.4: The characteristic polynomial and the dimension of eigenspaces
subsection 4.2.5: Using Sage to find eigenvalues and eigenvectors
subsection 4.2.6: Summary
section 4.3: Diagonalization, similarity, and powers of a matrix
subsection 4.3.1: Introduction
subsection 4.3.2: Diagonalization of matrices
subsection 4.3.3: Powers of a diagonalizable matrix
subsection 4.3.4: Similarity and complex eigenvalues
subsection 4.3.5: Summary
section 4.4: Dynamical systems
subsection 4.4.1: Introduction
subsection 4.4.2: A first example
subsection 4.4.3: Classifying dynamical systems
subsection 4.4.4: A $3\times3$ system
subsection 4.4.5: Summary
section 4.5: Markov chains and Google's PageRank algorithm
subsection 4.5.1: Introduction
subsection 4.5.2: A first example
subsection 4.5.3: Markov chains
subsection 4.5.4: Google's PageRank algorithm
subsection 4.5.5: Summary
chapter 5: Linear algebra and computing
section 5.1: Gaussian elimination revisited
subsection 5.1.1: Introduction
subsection 5.1.2: Partial pivoting
subsection 5.1.3: $LU$ factorizations
subsection 5.1.4: Summary
section 5.2: Finding eigenvectors numerically
subsection 5.2.1: Introduction
subsection 5.2.2: The power method
subsection 5.2.3: Finding other eigenvalues
subsection 5.2.4: Summary
chapter 6: Orthogonality and Least Squares
section 6.1: The dot product
subsection 6.1.1: Introduction
subsection 6.1.2: The geometry of the dot product
subsection 6.1.3: $k$-means clustering
subsection 6.1.4: Summary
section 6.2: Orthogonal complements and the matrix transpose
subsection 6.2.1: Introduction
subsection 6.2.2: Orthogonal complements
subsection 6.2.3: The matrix transpose
subsection 6.2.4: Properties of the matrix transpose
subsection 6.2.5: Summary
section 6.3: Orthogonal bases and projections
subsection 6.3.1: Introduction
subsection 6.3.2: Orthogonal sets
subsection 6.3.3: Orthogonal projections
subsection 6.3.4: Summary
section 6.4: Finding orthogonal bases
subsection 6.4.1: Introduction
subsection 6.4.2: Gram-Schmidt orthogonalization
subsection 6.4.3: $QR$ factorizations
subsection 6.4.4: Summary
section 6.5: Orthogonal least squares
subsection 6.5.1: Introduction
subsection 6.5.2: A first example
subsection 6.5.3: Solving least-squares problems
subsection 6.5.4: Using $QR$ factorizations
subsection 6.5.5: Polynomial Regression
subsection 6.5.6: Summary
chapter 7: Singular value decompositions
section 7.1: Symmetric matrices and variance
subsection 7.1.1: Introduction
subsection 7.1.2: Symmetric matrices and orthogonal diagonalization
subsection 7.1.3: Variance
subsection 7.1.4: Summary
section 7.2: Quadratic forms
subsection 7.2.1: Introduction
subsection 7.2.2: Quadratic forms
subsection 7.2.3: Definite symmetric matrices
subsection 7.2.4: Summary
section 7.3: Principal Component Analysis
subsection 7.3.1: Introduction
subsection 7.3.2: Principal Component Analysis
subsection 7.3.3: Using Principal Component Analysis
subsection 7.3.4: Summary
section 7.4: Singular Value Decompositions
subsection 7.4.1: Introduction
subsection 7.4.2: Finding singular value decompositions
subsection 7.4.3: The structure of singular value decompositions
subsection 7.4.4: Reduced singular value decompositions
subsection 7.4.5: Summary
section 7.5: Using Singular Value Decompositions
subsection 7.5.1: Introduction
subsection 7.5.2: Least-squares problems
subsection 7.5.3: Rank $k$ approximations
subsection 7.5.4: Principal component analysis
subsection 7.5.5: Image compressing and denoising
subsection 7.5.6: Analyzing Supreme Court cases
subsection 7.5.7: Summary
appendix A: Sage Reference

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
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1E7M33NVV8	exercise	exercise, section 4.5	austin_ula
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1Y9KSVT8EM	exercise	exercise, section 6.4	austin_ula
A subspace of $\real^4$	example	example, section 3.5.2	austin_ula
21GSYB9FQ9	statement	proposition, section 3.1.2	austin_ula
224C015AN6	exercise	exercise, section 2.4	austin_ula
23CFMKCSXA	exercise	exercise, section 3.3	austin_ula
23J2Y42M7B	exercise	exercise, section 5.1	austin_ula
25499HTR4E	exercise	exercise, section 6.5	austin_ula
2552FTHFG0	exercise	exploration, section 5.1.1	austin_ula
power method	concept	index, section 5.2.2	austin_ula
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row space	concept	index, section 7.4.3	austin_ula
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solution space	concept	index, section 1.1.2	austin_ula
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The equation $A\xvec = \bvec$	exercise	activity, section 2.2.3	austin_ula
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2Z424J79SF	exercise	activity, section 5.2.3	austin_ula
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characteristic equation	concept	index, section 4.2.2	austin_ula
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37Q3MQZPXH	exercise	exercise, section 4.3	austin_ula
395XRPNJH3	exercise	exercise, section 1.4	austin_ula
Discrete Fourier Transform	concept	index, section 3.3.3	austin_ula
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3FYEWNRK1C	example	example, section 4.2.4	austin_ula
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3HW935PM1S	exercise	exercise, section 1.2	austin_ula
3M1RJBXKVQ	exercise	exercise, section 6.4	austin_ula
Second Derivative Test	statement	proposition, section 7.2.3	austin_ula
state vector	concept	index, section 2.5.4	austin_ula
principal components	concept	index, section 7.3.2	austin_ula
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similarity	concept	index, section 4.3.4	austin_ula
normal equation	concept	index, section 6.5.3	austin_ula
407GDPFNKG	exercise	exercise, section 2.6	austin_ula
4394EGZNGY	exercise	exploration, section 6.3.1	austin_ula
459M2B3QBB	exercise	activity, section 3.4.3	austin_ula
45RJY68A59	exercise	exercise, section 4.3	austin_ula
45T5MHZ4PF	exercise	exercise, section 5.1	austin_ula
482WQPQVSE	definition	definition, section 4.5.3	austin_ula
48TSCQFHSH	exercise	exercise, section 3.2	austin_ula
49TKS90G1S	statement	proposition, section 1.4.2	austin_ula
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partial pivoting	concept	index, section 5.1.2	austin_ula
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4GW1CDR0Q9	example	example, section 7.4.2	austin_ula
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4MKN4B5P5B	exercise	exercise, section 7.2	austin_ula
4PHN9D74QA	exercise	exercise, section 2.2	austin_ula
4R01J2NNJK	exercise	exercise, section 2.3	austin_ula
4RW2AM81GB	exercise	exercise, section 3.1	austin_ula
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4WVT1ZGT8Z	exercise	exercise, section 6.2	austin_ula
4YG96DXZ2S	exercise	exercise, section 3.5	austin_ula
4YS319WRYB	definition	definition, section 3.5.4	austin_ula
positive matrix	concept	index, section 4.5.3	austin_ula
51GCYXVQW7	exercise	exercise, section 4.5	austin_ula
521SYJYSA0	exercise	exploration, section 3.1.1	austin_ula
53TC32TTRA	example	example, section 2.1.2	austin_ula
5540PBZEH1	exercise	exercise, section 7.4	austin_ula
55KQBBTNVH	exercise	exercise, section 6.1	austin_ula
55NZWAP7GF	exercise	exercise, section 3.1	austin_ula
589H8G36QG	example	example, section 3.1.2	austin_ula
58EXAMVHNT	exercise	activity, section 4.5.4	austin_ula
5AE7KEBJTQ	example	example, section 6.2.3	austin_ula
5B6VY6PW1P	example	example, section 1.2.1	austin_ula
5CDBFJ4M7B	exercise	exercise, section 3.2	austin_ula
5EDKZ2TCA5	exercise	activity, section 6.3.3	austin_ula
5FKY5ESBK5	example	example, section 6.3.2	austin_ula
5GX8SMDXDB	exercise	exercise, section 5.2	austin_ula
chrominance	concept	index, section 3.3.2	austin_ula
5MJG1T4MMC	exercise	activity, section 2.5.3	austin_ula
5Q4NBW7DR4	exercise	activity, section 7.4.3	austin_ula
5QP9K0CNDV	example	example, section 3.4.4	austin_ula
basis	concept	index, section 3.2.2	austin_ula
5XBS9NHCJF	example	example, section 7.2.2	austin_ula
5Z2M6BE46W	exercise	exercise, section 2.1	austin_ula
inconsistent system	concept	index, section 1.4.1	austin_ula
61K4B5VBH8	exercise	exercise, section 2.5	austin_ula
triangular system	concept	index, section 1.2.1	austin_ula
643NBWYS61	exercise	exercise, section 2.6	austin_ula
65185XBC4M	exercise	exercise, section 4.1	austin_ula
67AFN590EC	exercise	exercise, section 1.2	austin_ula
6885EMTTWZ	example	example, section 3.1.2	austin_ula
68TFK768AJ	exercise	exercise, section 1.2	austin_ula
6CA6N65QJQ	exercise	exercise, section 2.5	austin_ula
6CKQ6JH82X	statement	proposition, section 3.2.3	austin_ula
upper triangular matrix	concept	index, section 3.1.4	austin_ula
Projection formula	statement	proposition, section 6.3.3	austin_ula
Gaussian elimination and matrix multiplication	exercise	activity, section 3.1.4	austin_ula
6JAE31YZ5K	example	example, section 6.3.3	austin_ula
matrix, rank	concept	index, section 3.5.3	austin_ula
Scalar Multiplication and Vector Addition	exercise	exploration, section 2.1.1	austin_ula
6PK1G25X52	exercise	exercise, section 6.2	austin_ula
6QMV4SSK1G	exercise	exercise, section 4.1	austin_ula
6WBVVCTABF	exercise	activity, section 3.4.4	austin_ula
6WD65Q7AHW	example	question, section 4.1.3	austin_ula
6XDTJVAGV8	example	example, section 4.2.4	austin_ula
6Z0GCR9T5Z	exercise	exploration, section 2.6.1	austin_ula
orthogonal diagonalization	concept	index, section 7.1.2	austin_ula
The effect of row operations on the determinant	statement	proposition, section 3.4.3	austin_ula
727M9VZDNA	exercise	activity, section 3.3.2	austin_ula
72DR0XPSRA	exercise	activity, section 2.1.2	austin_ula
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Describing the solution space from a reduced row echelon matrix	example	example, section 1.2.3	austin_ula
7C5XV5PKZ4	example	example, section 3.2.4	austin_ula
weights	concept	index, section 2.1.2	austin_ula
7DSRPZ560Y	statement	theorem, section 7.4.3	austin_ula
7DVBWAJDVQ	statement	proposition, section 6.3.3	austin_ula
7EB8K47GJR	exercise	exercise, section 3.1	austin_ula
Subspaces of $\real^3$	example	example, section 3.5.2	austin_ula
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linearly dependent	concept	index, section 2.4.2	austin_ula
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The Spectral Theorem	statement	theorem, section 7.1.2	austin_ula
The singular value decomposition	statement	theorem, section 7.4.2	austin_ula
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83D7BVYNTM	exercise	exercise, section 2.1	austin_ula
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matrix transformation	concept	index, section 2.5.2	austin_ula
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85NQ6M3899	exercise	exercise, section 3.5	austin_ula
linear equation	concept	index, section 1.1.2	austin_ula
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null space	concept	index, section 3.5.4	austin_ula
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$QR$ factorization	statement	proposition, section 6.4.3	austin_ula
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matrix, identity	concept	index, section 2.2.1	austin_ula
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transition function	concept	index, section 2.5.4	austin_ula
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Linearity of matrix multiplication	statement	proposition, section 2.2.2	austin_ula
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AKVBRK33J5	exercise	exercise, section 5.1	austin_ula
matrix, addition	concept	index, section 2.2.1	austin_ula
The existence of solutions	exercise	exploration, section 2.3.1	austin_ula
AP7G72XKXZ	exercise	activity, section 2.6.3	austin_ula
APH1YXPF2R	definition	definition, section 4.5.2	austin_ula
AQRX0V60W7	exercise	exercise, section 3.3	austin_ula
ARHYX4BWJX	exercise	exploration, section 6.1.1	austin_ula
ATQMR75D2W	exercise	activity, section 7.3.2	austin_ula
AVHN7GWNP0	definition	definition, section 6.3.3	austin_ula
AVN20V0512	exercise	exercise, section 2.5	austin_ula
AWC4B9XNG4	exercise	exercise, section 7.5	austin_ula
stationary vector	concept	index, section 4.5.3	austin_ula
AX7XACDXEH	exercise	activity, section 3.5.2	austin_ula
AY90BVKP62	statement	proposition, section 7.5.2	austin_ula
AZQ3HP7D23	statement	proposition, section 6.2.3	austin_ula
AZSSSKHW3P	exercise	activity, section 6.1.3	austin_ula
B2MG2HGBZF	exercise	exercise, section 3.4	austin_ula
B4GPS118P4	statement	proposition, section 6.3.3	austin_ula
B789BSTJXS	exercise	exercise, section 3.4	austin_ula
B7XPBD19E8	exercise	exercise, section 3.5	austin_ula
BA8B0QTRG0	exercise	activity, section 2.2.2	austin_ula
unit vector	concept	index, section 6.3.2	austin_ula
round off error	concept	index, section 5.1.2	austin_ula
BKDYNY19FD	exercise	exercise, section 2.4	austin_ula
linear combination	concept	index, section 2.1.2	austin_ula
BR3F4MZ68C	exercise	exercise, section 7.5	austin_ula
BRE226SD50	exercise	exercise, section 6.5	austin_ula
orthogonal projection	concept	index, section 6.3.3	austin_ula
BS03MD58G5	statement	proposition, section 2.4.3	austin_ula
BTE1HTG762	example	example, section 4.3.3	austin_ula
BW3XGS8FAY	exercise	exercise, section 1.3	austin_ula
Linear combinations and linear systems	exercise	activity, section 2.1.2	austin_ula
BY408A74DY	exercise	activity, section 2.5.2	austin_ula
BZPGBW9QDS	statement	proposition, section 2.6.2	austin_ula
BZQN3ASJZK	statement	principle, section 1.4.3	austin_ula
C4BFW6APVZ	definition	definition, section 6.3.2	austin_ula
C5BWEMEBGS	exercise	exercise, section 6.5	austin_ula
C5Z826SKGB	exercise	activity, section 4.2.3	austin_ula
C7TDCZTPKP	exercise	exercise, section 6.2	austin_ula
C8N2R9MQ5F	exercise	exercise, section 5.1	austin_ula
CCQN932ZF2	example	example, section 6.3.3	austin_ula
CE3P4H3WVC	exercise	exercise, section 6.1	austin_ula
CFZC6XK07G	exercise	exercise, section 5.2	austin_ula
CGFW4719X9	definition	definition, section 2.3.2	austin_ula
Basic Sage commands	exercise	activity, section 1.3.1	austin_ula
CJD8SGANJ3	exercise	activity, section 7.5.3	austin_ula
CKCKF6C9F7	exercise	exercise, section 3.2	austin_ula
CKD7W4QYQV	exercise	exploration, section 7.3.1	austin_ula
CP669G1XAB	exercise	exercise, section 4.1	austin_ula
CPA6ZA33QQ	example	example, section 6.3.2	austin_ula
CQHAYH8FQ8	exercise	exercise, section 1.1	austin_ula
CT5Q14EDT9	exercise	activity, section 6.5.2	austin_ula
CV8NEA5HDD	exercise	exploration, section 3.3.1	austin_ula
CVMSN1W2KX	exercise	exercise, section 1.3	austin_ula
CXJYN81ETG	exercise	exploration, section 6.4.1	austin_ula
column space	concept	index, section 3.5.3	austin_ula
CYA99C2V3A	exercise	activity, section 7.2.2	austin_ula
CZ3ZCT7HCV	statement	proposition, section 2.3.3	austin_ula
CZPC6N1BVB	exercise	exercise, section 7.1	austin_ula
CZR3GYQ46Q	exercise	exercise, section 5.2	austin_ula
CZXPM4SZB3	example	example, section 5.2.2	austin_ula
D0DK73D7CF	exercise	exercise, section 2.4	austin_ula
invertible	concept	index, section 3.1.2	austin_ula
D4B3N05NHW	exercise	exercise, section 2.4	austin_ula
D594KCMCY6	example	example, section 5.2.2	austin_ula
scalar multiplication	concept	index, section 2.1.1	austin_ula
D70HCBTP7J	exercise	activity, section 1.1.1	austin_ula
D857VJ8HD9	exercise	exercise, section 6.3	austin_ula
D9KMEMCXMM	example	example, section 4.2.2	austin_ula
DA9RF830VF	exercise	exercise, section 3.2	austin_ula
Augmented matrices and solution spaces	exercise	activity, section 1.2.2	austin_ula
DBEDGXM0N0	exercise	exercise, section 7.1	austin_ula
DBN8GQZS7A	example	example, section 6.1.2	austin_ula
DE9M1177T5	exercise	activity, section 4.4.2	austin_ula
DKJ4Y7T4WM	example	example, section 7.2.2	austin_ula
DKK145MNNN	statement	proposition, section 6.5.3	austin_ula
DKS8A4WDT5	exercise	exercise, section 7.1	austin_ula
DM20910V8G	exercise	exercise, section 4.2	austin_ula
DMJKHGAPZY	exercise	activity, section 2.3.3	austin_ula
DPPRXFGD91	exercise	exercise, section 1.3	austin_ula
DTK2E9HY3Q	definition	definition, section 6.2.3	austin_ula
DWS97A23FH	exercise	activity, section 7.1.3	austin_ula
E0VYSXYMEJ	exercise	activity, section 4.5.3	austin_ula
E17FWG6ZP5	exercise	exercise, section 6.3	austin_ula
E3784Y7EED	exercise	exercise, section 3.5	austin_ula
E45RXMH8WB	statement	proposition, section 3.4.3	austin_ula
E4N08WMA6A	statement	proposition, section 3.5.4	austin_ula
E70BVE5ZF6	exercise	exercise, section 7.4	austin_ula
E72R622XBW	statement	proposition, section 7.1.2	austin_ula
E8Z71CHNBT	exercise	activity, section 4.5.3	austin_ula
EB4KYXEEJN	exercise	exercise, section 3.4	austin_ula
luminance	concept	index, section 3.3.2	austin_ula
EN005YKXRJ	example	example, section 3.2.4	austin_ula
EP2RWSY2W8	example	example, section 7.2.2	austin_ula
EQRQCH98RH	definition	definition, section 3.5.3	austin_ula
ET6QHJYT4K	exercise	exercise, section 7.4	austin_ula
Reduced singular value decomposition	statement	proposition, section 7.4.4	austin_ula
ETYDWZFZ0B	exercise	exercise, section 7.4	austin_ula
EV4VP14NZW	example	example, section 4.3.2	austin_ula
EZPVMWVMST	exercise	exercise, section 4.2	austin_ula
EZVZ4TFGSC	exercise	activity, section 3.3.3	austin_ula
consistent system	concept	index, section 1.4.1	austin_ula
F2P3WZEJDG	exercise	activity, section 2.5.2	austin_ula
F3GGWTGZRA	example	example, section 2.3.2	austin_ula
F3RFJ3VMGB	example	example, section 6.2.2	austin_ula
F46ZXN2N42	exercise	exercise, section 6.3	austin_ula
F66FZHJ6XB	statement	theorem, section 1.2.3	austin_ula
F6RWB5W7FP	exercise	exercise, section 6.4	austin_ula
F76G3SHHYF	exercise	exploration, section 5.2.1	austin_ula
F7QBRSP026	exercise	exploration, section 3.4.1	austin_ula
F8KP2677F0	example	example, section 7.1.2	austin_ula
FAX7EHWD5S	exercise	exercise, section 6.5	austin_ula
FBJ2206HN4	exercise	exercise, section 2.5	austin_ula
FC2VSYCJD2	statement	proposition, section 2.4.3	austin_ula
FEZ4Y9ZAE6	example	example, section 4.3.2	austin_ula
FFHP73J12Z	exercise	exercise, section 7.2	austin_ula
FJMATENXXQ	example	question, section 4.5.3	austin_ula
FNP399R4AS	exercise	exercise, section 6.2	austin_ula
FNTTDK32QT	exercise	activity, section 6.4.2	austin_ula
FQPYKXCPQZ	example	example, section 6.2.4	austin_ula
pivot position	concept	index, section 1.4.1	austin_ula
matrix-vector multiplication	concept	index, section 2.2.2	austin_ula
FVDCVTWTA9	exercise	exercise, section 6.2	austin_ula
FW3JGBF86G	exercise	exercise, section 5.1	austin_ula
FXD08SEXNY	exercise	exercise, section 2.5	austin_ula
FYCFWK9VMV	definition	definition, section 4.3.4	austin_ula
FYX80RH24W	statement	proposition, section 6.2.4	austin_ula
FZA493YX3P	exercise	activity, section 2.2.4	austin_ula
coefficient matrix	concept	index, section 1.2.2	austin_ula
G4PC9VBW03	exercise	exercise, section 4.5	austin_ula
G5FNVQKTQ9	exercise	activity, section 2.5.4	austin_ula
G6K798DFDE	exercise	exercise, section 4.5	austin_ula
decoupled system	concept	index, section 1.2.1	austin_ula
G7D7WBYQSC	exercise	exercise, section 5.2	austin_ula
G9M4TYQEYW	exercise	exercise, section 7.2	austin_ula
G9ZRHQMXF1	exercise	exercise, section 4.5	austin_ula
GA40S8MTFH	exercise	exercise, section 1.2	austin_ula
GC3EPHENDP	exercise	exercise, section 6.2	austin_ula
GD5J0MYC89	exercise	exercise, section 3.3	austin_ula
GE6Q5AQ6G4	statement	proposition, section 4.3.3	austin_ula
GFTRK372BK	example	example, section 3.2.2	austin_ula
GG9XGB1NJR	exercise	exercise, section 2.6	austin_ula
GH1RGJ5G9N	exercise	activity, section 7.2.2	austin_ula
GHSAK6Z42X	exercise	exercise, section 2.3	austin_ula
Matrix-vector multiplication	example	example, section 2.2.2	austin_ula
GMAYETNHZ8	exercise	activity, section 6.3.2	austin_ula
reduced row echelon matrix	concept	index, section 1.2.3	austin_ula
GR1BZH59XW	definition	definition, section 4.5.3	austin_ula
GTF3GN3PBW	definition	definition, section 1.1.2	austin_ula
GWB9Q5375S	exercise	activity, section 7.5.6	austin_ula
GXQRCWMYTB	exercise	exploration, section 2.4.1	austin_ula
GXZYHWC9CD	exercise	exercise, section 2.2	austin_ula
GY48RDNRN5	exercise	exercise, section 6.3	austin_ula
quadratic form	concept	index, section 7.2.2	austin_ula
GYTP5MGESP	exercise	exercise, section 4.1	austin_ula
GZ7CBTGQB8	exercise	exercise, section 5.1	austin_ula
H0MFNCT0EX	exercise	exercise, section 6.2	austin_ula
H0MXHSCNTS	exercise	exercise, section 6.5	austin_ula
H0VE174Y6X	exercise	exercise, section 4.5	austin_ula
H0Y3X8QCD5	exercise	activity, section 7.3.3	austin_ula
H6CMVZ5GYY	exercise	exercise, section 6.1	austin_ula
basis, standard	concept	index, section 3.2.2	austin_ula
HD698QN5CC	exercise	exercise, section 6.4	austin_ula
HDAWJVQXQ5	statement	proposition, section 4.3.2	austin_ula
HDRFG7FM3G	exercise	activity, section 3.1.2	austin_ula
HEMSMR9SQJ	exercise	exercise, section 2.2	austin_ula
HGGVGXR8C2	exercise	exercise, section 4.4	austin_ula
HHRBV8CR1Z	exercise	exercise, section 2.2	austin_ula
HHWG1TEW2B	example	example, section 2.4.2	austin_ula
HKBQHZ00FX	statement	proposition, section 7.1.3	austin_ula
HNY5QBZ607	statement	proposition, section 3.4.3	austin_ula
HRRZM039B7	exercise	exercise, section 2.4	austin_ula
Linear independence and homogeneous equations	exercise	activity, section 2.4.4	austin_ula
HWX3TE6M1Y	statement	proposition, section 6.5.4	austin_ula
HY3KQW2JWC	exercise	exploration, section 1.2.1	austin_ula
HZEM46TYCN	exercise	activity, section 4.2.2	austin_ula
J011BJ81X4	exercise	activity, section 1.4.2	austin_ula
J0A32XZHS0	example	example, section 4.2.4	austin_ula
J14C6CCEBJ	exercise	exercise, section 7.2	austin_ula
J15RXP2GKC	exercise	exercise, section 2.5	austin_ula
rank	concept	index, section 3.5.3	austin_ula
J3YE658MDY	exercise	activity, section 4.3.3	austin_ula
J8FBXWQDNC	exercise	exercise, section 7.5	austin_ula
othonormal set	concept	index, section 6.3.2	austin_ula
J8R1JSE700	exercise	exploration, section 4.4.1	austin_ula
JAHFBDCXZ8	exercise	activity, section 7.4.2	austin_ula
JBYC0VM1RH	definition	definition, section 1.1.2	austin_ula
JC3K4Z1Y63	exercise	activity, section 7.2.3	austin_ula
JCK8FAGTFZ	exercise	activity, section 5.1.3	austin_ula
JCKX2MXJNV	statement	proposition, section 3.2.2	austin_ula
JCT42FFJ67	exercise	activity, section 2.3.2	austin_ula
JFN7XMA05D	exercise	exercise, section 6.1	austin_ula
JFR1BSN6B4	exercise	exercise, section 1.1	austin_ula
JHFHQXM5AD	exercise	activity, section 6.5.4	austin_ula
JJ7C8MAKY7	exercise	exercise, section 2.1	austin_ula
eigenvalue, dominant	concept	index, section 5.2.2	austin_ula
JM6HTY0JJ0	exercise	exercise, section 3.1	austin_ula
JQ489KKZPW	exercise	exercise, section 7.4	austin_ula
JRMBJS2YAV	exercise	exercise, section 7.3	austin_ula
JT877FA4CX	exercise	activity, section 6.4.2	austin_ula
JTAVN2G5AB	definition	definition, section 7.2.3	austin_ula
JVGW43S19J	statement	proposition, section 7.4.3	austin_ula
JWKMYE32WR	exercise	exercise, section 6.2	austin_ula
JY7HQ1CRMN	exercise	exercise, section 2.3	austin_ula
K3NBQ5HNN9	statement	proposition, section 7.2.3	austin_ula
K4KWXMVPGN	exercise	exercise, section 3.1	austin_ula
lower triangular matrix	concept	index, section 3.1.4	austin_ula
K5N9TFG6KE	exercise	exercise, section 7.2	austin_ula
K5RF59BT65	exercise	exercise, section 7.3	austin_ula
back substitution	concept	index, section 1.2.1	austin_ula
K9Y4Q59TDN	exercise	exercise, section 4.4	austin_ula
KARER3N9SN	exercise	exercise, section 4.4	austin_ula
KBNKWQG6ZT	exercise	exercise, section 2.5	austin_ula
KH008NPNNP	exercise	exercise, section 3.1	austin_ula
KH3GJTPS7Z	exercise	exercise, section 4.3	austin_ula
KHDTFYPJMG	exercise	activity, section 7.5.2	austin_ula
KJVWNNZA9S	exercise	exercise, section 3.2	austin_ula
KKJAKHVHNC	exercise	exercise, section 6.4	austin_ula
KQ6TVB9701	example	example, section 2.4.4	austin_ula
KQZS5X71ER	exercise	exercise, section 1.3	austin_ula
KTH8N8DV9T	exercise	exercise, section 7.1	austin_ula
vector	concept	index, section 2.1.1	austin_ula
KVY7BQHJHN	exercise	exercise, section 4.5	austin_ula
KVYZVHTK0J	exercise	activity, section 1.1.1	austin_ula
vector addition	concept	index, section 2.1.1	austin_ula
determinant	concept	index, section 3.4.2	austin_ula
M0JWVN77DV	example	example, section 7.2.2	austin_ula
M37E5C51A3	definition	definition, section 4.3.2	austin_ula
M41WRNGQ79	exercise	activity, section 3.2.3	austin_ula
M4S13FVMAB	example	example, section 2.5.2	austin_ula
M50RSBDH9Z	exercise	exercise, section 1.4	austin_ula
span	concept	index, section 2.3.2	austin_ula
M71H6TA48F	example	example, section 7.1.2	austin_ula
MA5QBMDXPY	exercise	exploration, section 3.2.1	austin_ula
MAK4M2NRQ5	exercise	exercise, section 6.1	austin_ula
MCA985339Y	statement	proposition, section 7.2.2	austin_ula
linear system	concept	index, section 1.1.2	austin_ula
multiplicity	concept	index, section 4.2.4	austin_ula
Properties of invertible matrices	statement	proposition, section 3.1.3	austin_ula
MQB7F07AYG	exercise	exercise, section 6.3	austin_ula
MR34FNHE1F	exercise	activity, section 4.4.3	austin_ula
MR50JQ10PA	exercise	exploration, section 7.1.1	austin_ula
MRQZGNQDQG	exercise	exercise, section 3.4	austin_ula
MVK9DH75EJ	statement	proposition, section 2.1.2	austin_ula
steady-state vector	concept	index, section 4.5.3	austin_ula
MWXTE1T1FN	exercise	exercise, section 2.5	austin_ula
N3GA4RQP9G	definition	definition, section 2.4.2	austin_ula
N5SQ3DRZ6Q	exercise	exercise, section 3.4	austin_ula
N6K6YJ0W0Q	exercise	exercise, section 3.3	austin_ula
N6QS916Y50	statement	proposition, section 2.4.4	austin_ula
N7BZ8ZF7Z6	exercise	exercise, section 6.5	austin_ula
Matrix-vector multiplication	definition	definition, section 2.2.2	austin_ula
NA1WT4408W	exercise	activity, section 1.4.3	austin_ula
NBDCPXW48D	exercise	exercise, section 4.5	austin_ula
NCGNVG9K7S	example	example, section 4.2.4	austin_ula
NCKBZN5SY3	exercise	exercise, section 2.2	austin_ula
ND21HK8YGY	example	example, section 3.5.3	austin_ula
Gram matrix	concept	index, section 7.4.2	austin_ula
Perron-Frobenius	statement	theorem, section 4.5.3	austin_ula
NEEGSDZZA9	exercise	exercise, section 7.2	austin_ula
eigenvalue	concept	index, section 4.1.2	austin_ula
NG3TNY8HS8	statement	proposition, section 7.4.2	austin_ula
NGJKWPB6VB	exercise	exploration, section 7.2.1	austin_ula
NH000CR28N	exercise	exercise, section 7.2	austin_ula
Matrix-vector multiplication	exercise	activity, section 2.2.2	austin_ula
NK1MBNY0F6	example	example, section 2.5.2	austin_ula
NMNM2GDDMY	exercise	activity, section 7.1.3	austin_ula
NPQ927612B	exercise	exercise, section 2.6	austin_ula
NRJ3MAYQ62	exercise	exercise, section 7.3	austin_ula
eigenspace	concept	index, section 4.2.3	austin_ula
NSYQWTKYTV	exercise	exercise, section 7.2	austin_ula
NVM6P287QP	exercise	exercise, section 4.4	austin_ula
NXK157JPDA	exercise	exercise, section 2.3	austin_ula
NZHST3QAQT	example	example, section 6.2.3	austin_ula
diagonalizable	concept	index, section 4.3.2	austin_ula
P7R3N6VVQ6	exercise	exercise, section 4.3	austin_ula
P8H6HQTKTB	exercise	exercise, section 6.2	austin_ula
PAR1YZN22A	exercise	exercise, section 1.4	austin_ula
linearly independent	concept	index, section 2.4.2	austin_ula
PDF233EJBS	exercise	exercise, section 7.1	austin_ula
PDXHCF7PVR	exercise	exercise, section 7.2	austin_ula
PG6XBGP86K	statement	proposition, section 3.4.2	austin_ula
PP978F4CHE	exercise	activity, section 5.2.3	austin_ula
PPFTYCC28J	statement	proposition, section 2.5.3	austin_ula
Vectors in $W$ and $W^\perp$	exercise	exercise, section 6.2.5	austin_ula
PPKNQM79BH	exercise	exercise, section 4.1	austin_ula
PQPJ7GD82S	example	example, section 6.1.2	austin_ula
PRJK3AWN8N	definition	definition, section 3.1.2	austin_ula
dimension	concept	index, section 3.5.2	austin_ula
PT4HCQKK79	exercise	exercise, section 4.4	austin_ula
PT76NRK75A	exercise	activity, section 6.5.3	austin_ula
PTYQ11JFRX	exercise	exploration, section 4.1.1	austin_ula
PV4RATVB9P	exercise	exercise, section 4.3	austin_ula
PVB1ARKB4V	exercise	exercise, section 2.3	austin_ula
PVTK475A7Z	exercise	exercise, section 7.4	austin_ula
PYA9G3F9FF	example	example, section 4.2.3	austin_ula
reduced row echelon form	concept	index, section 1.2.3	austin_ula
Q0ERJSJTE4	exercise	exercise, section 6.1	austin_ula
Q17N012ZED	example	example, section 6.4.2	austin_ula
matrix, scalar multiplication	concept	index, section 2.2.1	austin_ula
dot product	concept	index, section 6.1.2	austin_ula
probability vector	concept	index, section 4.5.2	austin_ula
Q4KCR7WV8Y	exercise	exercise, section 5.2	austin_ula
Two Fundamental Questions	example	question, section 1.4.1	austin_ula
Q7QCJR5BB7	statement	proposition, section 3.1.4	austin_ula
QKQ02WAC0F	statement	proposition, section 3.1.2	austin_ula
matrix, square	concept	index, section 3.1.2	austin_ula
QPQ0ZEQ9CF	exercise	activity, section 3.4.2	austin_ula
QPXY8QN6WH	exercise	exercise, section 4.1	austin_ula
Gram-Schmidt	concept	index, section 6.4.2	austin_ula
QQXERE3BRG	exercise	exercise, section 4.4	austin_ula
QR387XHGN2	exercise	exercise, section 6.4	austin_ula
QRJ87399F2	exercise	activity, section 4.3.4	austin_ula
QRNR9PGQXV	exercise	exercise, section 6.5	austin_ula
QTKA6F297G	example	example, section 6.2.4	austin_ula
QTZEZDJ0JM	exercise	activity, section 7.1.3	austin_ula
QW8PTTWC5H	exercise	activity, section 4.4.3	austin_ula
matrix, inverse	concept	index, section 3.1.2	austin_ula
Principal Axes Theorem	statement	theorem, section 7.2.2	austin_ula
free variable	concept	index, section 1.2.3	austin_ula
R5BV0S8X3D	exercise	exercise, section 5.2	austin_ula
Linear equations and their solutions	exercise	activity, section 1.1.2	austin_ula
R7JJV2R1QQ	exercise	exercise, section 6.3	austin_ula
RB2X4Q9JY3	exercise	exercise, section 7.4	austin_ula
RBSJBM8MDQ	exercise	exploration, section 4.3.1	austin_ula
RCQZH3R2C4	exercise	exercise, section 3.1	austin_ula
RE91FWEXS8	exercise	exercise, section 7.1	austin_ula
RG5PEXXFKN	example	example, section 4.3.2	austin_ula
RHXRJJTJK6	exercise	exercise, section 7.4	austin_ula
RJW0J0RRKF	example	example, section 4.5.3	austin_ula
RKYVPYCSAM	exercise	exercise, section 2.1	austin_ula
RKZXNGEH7A	exercise	exercise, section 2.2	austin_ula
RMJMAF9N6C	exercise	activity, section 6.1.3	austin_ula
RQX9X96FBZ	exercise	exercise, section 1.2	austin_ula
RS90FZESEP	exercise	activity, section 6.5.5	austin_ula
RTKG3NAGMP	example	example, section 4.2.3	austin_ula
Edge detection	exercise	activity, section 3.2.4	austin_ula
RVZH21WXK2	exercise	exploration, section 7.4.1	austin_ula
RYAGRG1133	exercise	exercise, section 5.1	austin_ula
S0HM2X6XYF	definition	definition, section 1.4.1	austin_ula
S1GK09M38K	exercise	exercise, section 3.4	austin_ula
S1R735K4GX	example	example, section 2.2.4	austin_ula
eigenvector	concept	index, section 4.1.2	austin_ula
R squared	concept	index, section 6.5.3	austin_ula
S3EE1YA6VF	example	example, section 3.4.2	austin_ula
S722GGSSJY	exercise	activity, section 6.5.5	austin_ula
SAV74R90EQ	exercise	exercise, section 2.2	austin_ula
SDS918SYQT	exercise	activity, section 6.2.4	austin_ula
SET3034E46	statement	proposition, section 4.3.4	austin_ula
SETT55VNGM	statement	proposition, section 4.2.4	austin_ula
SKV4WRBFED	exercise	exercise, section 6.1	austin_ula
SPQMXWR5XC	exercise	activity, section 7.3.3	austin_ula
SPTS0CGSQM	exercise	exercise, section 4.2	austin_ula
SQ79TSC22K	exercise	exercise, section 3.3	austin_ula
SRGD98EA07	exercise	exercise, section 4.4	austin_ula
matrix, shape	concept	index, section 2.2.1	austin_ula
SSB7C7ADCZ	exercise	exercise, section 2.3	austin_ula
T1V41VPA2Q	example	example, section 2.3.2	austin_ula
T3H0F1GG1K	definition	definition, section 3.5.2	austin_ula
T979VNBD7E	exercise	activity, section 5.1.2	austin_ula
TAHQXPJ0R0	exercise	exploration, section 2.5.1	austin_ula
TBVX3SJ024	exercise	exercise, section 3.2	austin_ula
TDV4EFJ69V	exercise	exercise, section 6.5	austin_ula
TFQPXK1NAY	statement	proposition, section 6.2.3	austin_ula
TFTC9CNWMD	exercise	exercise, section 3.4	austin_ula
TGS000PD8Y	example	example, section 5.1.3	austin_ula
THP37Q3ZNN	exercise	exercise, section 7.1	austin_ula
Additivity of Variance	statement	proposition, section 7.1.3	austin_ula
basic variable	concept	index, section 1.2.3	austin_ula
TN3Y6P6TFC	exercise	exercise, section 2.3	austin_ula
Matrix-matrix multiplication	definition	definition, section 2.2.4	austin_ula
Markov chain	concept	index, section 4.5.3	austin_ula
TRCXK6NB2Q	example	example, section 7.4.2	austin_ula
orthogonal	concept	index, section 6.1.2	austin_ula
TSKD793W3Z	exercise	exercise, section 3.1	austin_ula
TSX20JCQFP	exercise	exercise, section 4.4	austin_ula
TTPFCQBYFM	exercise	exercise, section 2.1	austin_ula
TXDF4TK1W2	definition	definition, section 3.4.2	austin_ula
TZ7519C5R0	exercise	exercise, section 7.5	austin_ula
V3FDWTXJYY	exercise	exercise, section 7.3	austin_ula
V4FPNMPTSR	exercise	exercise, section 3.5	austin_ula
V95XDS8M8J	exercise	exercise, section 6.5	austin_ula
VB9YBDDV86	exercise	exercise, section 2.2	austin_ula
VC9D07V8PB	exercise	exercise, section 4.3	austin_ula
VCF4SM9989	exercise	exercise, section 5.2	austin_ula
VDE53WZQX8	example	example, section 2.4.2	austin_ula
VE8ZM3D80Y	exercise	exercise, section 7.5	austin_ula
VJ46CAEJKJ	example	example, section 2.1.2	austin_ula
VJHG99DTGM	example	example, section 7.1.2	austin_ula
VP7YV5CVZS	exercise	activity, section 4.4.4	austin_ula
VP84JZWQZC	example	example, section 7.4.3	austin_ula
transpose	concept	index, section 6.2.3	austin_ula
orthogonal set	concept	index, section 6.3.2	austin_ula
W0ZE09VMNV	exercise	exercise, section 2.1	austin_ula
W1A9GB3ABQ	exercise	activity, section 6.1.2	austin_ula
W30WSJP5P4	exercise	exploration, section 4.5.1	austin_ula
W3FFQXSSGY	example	example, section 3.5.4	austin_ula
W3GPQWX98E	exercise	exercise, section 4.2	austin_ula
Gaussian elimination	concept	index, section 1.2.1	austin_ula
W6DRG55B5A	exercise	exercise, section 1.3	austin_ula
W6FGH3D1WS	exercise	activity, section 7.4.2	austin_ula
W7TK3AYYK6	exercise	exercise, section 3.1	austin_ula
W7VGR718XW	example	example, section 6.3.2	austin_ula
subspace	concept	index, section 3.5.2	austin_ula
W9NQJ9VPHY	exercise	exercise, section 1.2	austin_ula
W9VNP2JXW8	definition	definition, section 3.5.3	austin_ula
WB2QCHSDHN	exercise	activity, section 4.5.4	austin_ula
WEN6CGSFSB	statement	proposition, section 4.2.4	austin_ula
WG8JW730JA	exercise	exercise, section 3.5	austin_ula
WJY40RN148	exercise	exercise, section 2.3	austin_ula
WK0FJX8YR4	exercise	exercise, section 1.1	austin_ula
orthogonal complement	concept	index, section 6.2.2	austin_ula
Matrix operations	exercise	exploration, section 2.2.1	austin_ula
WQC15XAHPY	definition	definition, section 7.1.2	austin_ula
characteristic polynomial	concept	index, section 4.2.2	austin_ula
matrix, elementary	concept	index, section 3.1.4	austin_ula
WVPZ1BYDAN	exercise	exercise, section 6.4	austin_ula
WX45PCG65K	definition	definition, section 6.2.2	austin_ula
WZ7S54JK7D	exercise	exercise, section 3.4	austin_ula
X19TZKZCD1	exercise	activity, section 7.3.2	austin_ula
X1KK8BNZJ0	exercise	exercise, section 4.1	austin_ula
X2MKYV0FQH	exercise	activity, section 3.2.2	austin_ula
X35E652BG9	exercise	exercise, section 5.1	austin_ula
row equivalent	concept	index, section 1.2.2	austin_ula
X6R4AWYGGC	exercise	exercise, section 2.2	austin_ula
X7P09P9X5G	exercise	exercise, section 2.4	austin_ula
X91V4QNC09	exercise	exercise, section 6.3	austin_ula
solution	concept	index, section 1.1.2	austin_ula
XB1ER6KQ4D	exercise	exercise, section 6.1	austin_ula
XBEPP4CYG0	exercise	exercise, section 7.4	austin_ula
XDA35JRZCX	exercise	exercise, section 4.2	austin_ula
XDGBXER9PW	example	example, section 4.2.2	austin_ula
XE5JZPW0ZE	exercise	exercise, section 6.3	austin_ula
discrete dynamical system	concept	index, section 2.5.4	austin_ula
XGS19TJEAE	example	example, section 4.3.2	austin_ula
XM6MH1BSF0	example	example, section 4.2.2	austin_ula
XMA0BKFX5F	exercise	exercise, section 7.3	austin_ula
XP8XR0F2GG	exercise	exercise, section 7.1	austin_ula
XQDV7NGTQC	exercise	exercise, section 2.5	austin_ula
XQS9QF1J6M	exercise	exercise, section 6.3	austin_ula
XS1PYSGM33	definition	definition, section 3.1.4	austin_ula
XXHTS4X42H	exercise	exercise, section 2.4	austin_ula
Moore-Penrose psuedoinverse	concept	index, section 7.5.2	austin_ula
Y0WWRTHMWK	exercise	activity, section 6.4.3	austin_ula
Y14KN20M06	exercise	exercise, section 1.1	austin_ula
Y17F560WEX	exercise	activity, section 4.2.5	austin_ula
Y1EDT845M6	exercise	exercise, section 3.4	austin_ula
Y2V1CKEDKE	exercise	exercise, section 3.1	austin_ula
Y3W5YCM3AS	exercise	exercise, section 7.1	austin_ula
Y699Y6T06Y	exercise	exercise, section 1.4	austin_ula
Y82Q4952NR	example	example, section 4.2.4	austin_ula
$YC_bC_r$ color model	concept	index, section 3.3.2	austin_ula
YB4S3R1QHX	exercise	activity, section 7.1.2	austin_ula
YC8XN6727V	statement	proposition, section 3.5.4	austin_ula
YE025CTFYW	exercise	exercise, section 6.1	austin_ula
augmented matrix	concept	index, section 1.2.2	austin_ula
stochastic matrix	concept	index, section 4.5.2	austin_ula
YF4T5G5QCZ	exercise	exercise, section 6.5	austin_ula
YNFF4DB5XP	exercise	activity, section 4.5.2	austin_ula
orthogonal matrix	concept	index, section 6.3.3	austin_ula
YQ3ZSPMBG9	example	example, section 6.3.3	austin_ula
YQ6F1H7JKQ	exercise	exercise, section 5.2	austin_ula
YRDXCV2D1E	exercise	exercise, section 3.5	austin_ula
YSB4D6BD8X	exercise	exercise, section 1.4	austin_ula
Using matrix transformations to describe geometric operations	exercise	activity, section 2.6.2	austin_ula
YZ70JRCHXN	statement	proposition, section 4.3.2	austin_ula
Z038QDP0YD	exercise	exercise, section 7.5	austin_ula
Z05PYWPPY8	exercise	exercise, section 7.4	austin_ula
Z2EXGZJQNZ	exercise	exercise, section 4.3	austin_ula
Z2XHGVXPRN	exercise	exercise, section 3.1	austin_ula
Z531GYK0Q0	exercise	exploration, section 7.5.1	austin_ula
$RGB$ color model	concept	index, section 3.3.2	austin_ula
Z8DNYF99VC	exercise	exercise, section 3.5	austin_ula
parametric description	concept	index, section 1.2.3	austin_ula
Some basic observations about pivots	exercise	exploration, section 1.4.1	austin_ula
Z90XY3PGNK	exercise	exercise, section 2.3	austin_ula
Coefficient of determination	definition	definition, section 6.5.3	austin_ula
ZA1C0ND684	example	example, section 4.1.2	austin_ula
ZAMNKVWZ8F	exercise	exercise, section 5.2	austin_ula
ZBRG7WR8VV	exercise	exercise, section 1.4	austin_ula
ZBT31EDP2T	exercise	exercise, section 3.5	austin_ula
ZC66MB23XD	exercise	exercise, section 3.4	austin_ula
ZD1VGSQ3DH	example	example, section 4.2.4	austin_ula
ZEM470XVCA	definition	definition, section 6.3.2	austin_ula
coefficient of determination	concept	index, section 6.5.3	austin_ula
ZN827NEKZ9	exercise	activity, section 4.1.2	austin_ula
Augmentation Principle	statement	proposition, section 1.3.2	austin_ula
ZQJWQ3BW21	exercise	exercise, section 2.2	austin_ula
ZSD2P1V1TH	exercise	activity, section 6.4.3	austin_ula
ZW0MCGCKPH	example	example, section 7.4.4	austin_ula
ZWZJKQ0HJ0	definition	definition, section 3.2.2	austin_ula
ZXN8VNJHRY	exercise	activity, section 6.1.2	austin_ula
ZY51ZHGA5K	exercise	exercise, section 4.4	austin_ula

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austin_ula: austin_ula (work)