NOC:Linear Algebra


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...)