Linear Algebra AQFT27XT6H

URI	`m2://res/AQFT27XT6H`
Kind	course
Creators	Dilip P. Patil (instructor)
Date	2017-01-17
Scope	in
Ids	course 04dese585:111108098

Expressions

e1: edition

Language	en
Date	2017-01-17

m1: page, IISc Bangalore (record). nptel 111108098
m2: page, 2017-01-17 (record). nptel 111108098

Contents

part 1: Week1
session 1: Introduction to Algebraic Structures - Rings and Fields
session 2: Definition of Vector Spaces
session 3: Examples of Vector Spaces
session 4: Definition of subspaces
session 5: Examples of subspaces
part 2: Week 2
session 6: Examples of subspaces (continued)
session 7: Sum of subspaces
session 8: System of linear equations
session 9: Gauss elimination
session 10: Generating system , linear independence and bases
part 3: Week3
session 11: Examples of a basis of a vector space
session 12: Review of univariate polynomials
session 13: Examples of univariate polynomials and rational functions
session 14: More examples of a basis of vector spaces
session 15: Vector spaces with finite generating system
part 4: Week 4
session 16: Steinitzs exchange theorem and examples
session 17: Examples of finite dimensional vector spaces
session 18: Dimension formula and its examples
session 19: Existence of a basis
session 20: Existence of a basis (continued)
part 5: Week 5
session 21: Existence of a basis [continued]
session 22: Introduction to Linear Maps
session 23: Examples of Linear Maps
session 24: Linear Maps and Bases
session 25: Pigeonhole principle in Linear Algebra
part 6: Week 6
session 26: Interpolation and the rank theorem
session 27: Examples
session 28: Direct sums of vector spaces
session 29: Projections
session 30: Direct sum decomposition of a vector space
part 7: Week 7
session 31: Dimension equality and examples
session 32: Dual spaces
session 33: Dual spaces (continued)
session 34: Quotient spaces
session 35: Homomorphism theorem of vector spaces
part 8: Week 8
session 36: Isomorphism theorem of vector spaces
session 37: Matrix of a linear map
session 38: Matrix of a linear map (continued)
session 39: Matrix of a linear map [continued]
session 40: Change of bases
part 9: Week 9
session 41: Computational rules for matrices
session 42: Rank of a matrix
session 43: Computation of the rank of a matrix
session 44: Elementary matrices
session 45: Elementary operations on matrices
part 10: Week 10
session 46: LR decomposition
session 47: Elementary Divisor Theorem
session 48: Permutation groups
session 49: Canonical cycle decomposition of permutations
session 50: Signature of a permutation
part 11: Week 11
session 51: Introduction to multilinear maps
session 52: Multilinear maps (continued)
session 53: Introduction to determinants
session 54: Determinants (continued)
session 55: Computational rules for determinants
part 12: Week 12
session 56: Properties of determinants and adjoint of a matrix
session 57: Adjoint-determinant theorem
session 58: The determinant of a linear operator
session 59: Determinants and Volumes
session 60: Determinants and Volumes (continued)

Catalogue records

nptel: 111108098 (manifestation)
nptel_video: 111108098 (manifestation)