E0 219          LINEAR ALGEBRA AND APPLICATIONS            AUG--DEC 2016

Professor D. P. Patil
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Lecture Notes 

No/Date Topics 
1A  Algebraic Structures
1B  Vector Spaces
1C  Subspaces
2  Linear Equations
3A  Generating Systems, Linear independence and Bases
3B  Dimension of Vector Spaces
5A  Group homomorphisms
5B  Linear maps
5C  Space of Linear maps
5D  Linear maps and Bases
5E  The Rank Theorem
5F  Direct sums and Projections
5F  Direct sums and Projections
5G  Dual spaces
6B  Quotient spaces
6E  Operations of groups
8A  The matrix of a linear map
8B  Rank of matrices
8C  Elementary matrices
9A  Permutation Groups
9B  Multilinear Maps
9C  Determinant Functions
9D  Computational Rules for Determinants
9E  The Determinants of a Linear Operator
9F  Orientations
10A  Polynomials in one variable
10B  Polynomials in several variables
11A  Eigenvalues, Characteristic polynomial and Minimal polynomial
11B  Diagonalizable and Trigonalizable operators
11C  Some decompositions theorems
11D  Jordan normal form

Progress of Lectures 

Lect 1 Lect 2
Jan 04 Introductory Lecture
Jan 04 Polynomials