Linear Algebra JQD5MMP63F

URI	`m2://res/JQD5MMP63F`
Kind	course
Creators	Arbind Kumar Lal (instructor)
Date	2020-08-31
Scope	in
Ids	course 05pjsgx75:111104137

Expressions

e1: edition

Language	en
Date	2020-08-31

m1: page, IIT Kanpur (record). nptel 111104137
m2: page, 2020-08-31 (record). nptel 111104137

Contents

part 1: Week 1
session 1: Notations, Motivation and Definition
session 2: Matrix: Examples, Transpose and Addition
session 3: Matrix Multiplication
session 4: Matrix Product Recalled
session 5: Matrix Product Continued
session 6: Inverse of a Matrix
part 2: Week 2
session 7: Introduction to System of Linear Equations
session 8: Some Initial Results on Linear Systems
session 9: Row Echelon Form (REF)
session 10: LU Decomposition - Simplest Form
session 11: Elementary Matrices
session 12: Row Reduced Echelon Form (RREF)
session 13: Row Reduced Echelon Form (RREF) Continued
session 14: RREF and Inverse
part 3: Week 3
session 15: Rank of a matrix
session 16: Solution Set of a System of Linear Equations
session 17: System of n Linear Equations in n Unknowns
session 18: Determinant
session 19: Permutations and the Inverse of a Matrix
session 20: Inverse and the Cramer's Rule
part 4: Week 4
session 21: Vector Spaces
session 22: Vector Subspaces and Linear Span
session 23: Linear Combination, Linear Independence and Dependence
session 24: Basic Results on Linear Independence
session 25: Results on Linear Independence Continued...
part 5: Week 5
session 26: Basis of a Finite Dimensional Vector Space
session 27: Fundamental Spaces associated with a Matrix
session 28: Rank - Nullity Theorem
session 29: Fundamental Theorem of Linear Algebra
part 6: Week 6
session 30: Definition and Examples of Linear Transformations
session 31: Results on Linear Transformations
session 32: Rank-Nullity Theorem and Applications
session 33: Isomorphism of Vector Spaces
session 34: Ordered Basis of a Finite Dimensional Vector Space
part 7: Week 7
session 35: Ordered Basis Continued
session 36: Matrix of a Linear transformation
session 37: Matrix of a Linear transformation Continued...
session 38: Matrix of Linear Transformations Continued...
session 39: Similarity of Matrices
part 8: Week 8
session 40: Inner Product Space
session 41: Inner Product Continued
session 42: Cauchy Schwartz Inequality
session 43: Projection on a Vector
session 44: Results on Orthogonality
session 45: Results on Orthogonality.
part 9: Week 9
session 46: Gram-Schmidt Orthonormalization Process
session 47: Orthogonal Projections
session 48: Gram-Schmidt Process: Applications
session 49: Examples and Applications on QR-decomposition
session 50: Recapitulate ideas on Inner Product Spaces
part 10: Week 10
session 51: Motivation on Eigenvalues and Eigenvectors
session 52: Examples and Introduction to Eigenvalues and Eigenvectors
session 53: Results on Eigenvalues and Eigenvectors
session 54: Results on Eigenvalues and Eigenvectors
session 55: Results on Eigenvalues and Eigenvectors.
part 11: Week 11
session 56: Diagonalizability
session 57: Diagonalizability Continued...
session 58: Schur's Unitary Triangularization (SUT)
session 59: Applications of Schur's Unitary Triangularization
session 60: Spectral Theorem for Hermitian Matrices
session 61: Cayley Hamilton Theorem
part 12: Week 12
session 62: Quadratic Forms
session 63: Sylvester's Law of Inertia
session 64: Applications of Quadratic Forms to Analytic Geometry
session 65: Examples of Conics and Quartics
session 66: Singular Value Decomposition (SVD)
part 13: Live Session
session 67: Live Session 20-10-2020

Catalogue records

nptel: 111104137 (manifestation)
nptel_video: 111104137 (manifestation)