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