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MA409 Advanced Linear Algebra

Course Plan

Lecture Notes

• L-01 Vector Spaces
• L-02 Linear Independence and Basis
• L-03 Matrices and Gaussian Elimination (Part - 1)
• L-04 Matrices and Gaussian Elimination (Part - 2)
• L-05 Linear Transformations
• L-06 Existence of Left/Right/Two-sided Inverses
• L-07 Determinants
• L-08 Quotient Spaces
• L-09 Rank Factorization
• L-10 Inner Product and Orthogonality
• L-11 Gram Schmidt Orthogonalization Process
• L-12 Eigenvalues and Eigenvectors
• L-13 Orthogonal Projector

Problem Sheets

• PS-01 Vector Spaces
• PS-02 Subspaces
• PS-03 Linear Combinations
• PS-04 Linear Dependence and Linear Independence
• PS-05 Bases and Dimension
• PS-06 Linear Transformations, Null Spaces, and Ranges
• PS-07 Matrix Representation of a Linear Transformation
• PS-08 Composition of Linear Transformations and Matrix Multiplication
• PS-09 Invertibility and Isomorphism
• PS-10 The Change of Coordinate Matrix
• PS-11 Elementary Matrix and Elementary Matrices
• PS-12 The Rank of a Matrix and Matrix Inverses
• PS-13 Systems of Linear Equations Theoretical Aspects
• PS-14 Systems of Linear Equations - Computational Aspects
• PS-15 Determinants of order 2
• PS-16 Determinants of order n
• PS-17 Properties of Determinants
• PS-18 Important Facts about Determinants
• PS-19 Eigenvalues and Eigenvectors
• PS-20 Diagonalizability
• PS-21 Invariant Subspaces and the Cayley-Hamilton Theorem
• PS-22 Inner Products and Norms
• PS-23 Gram-Schmidt Orthogonalization Process
• PS-24 The Adjoint of a Linear Operator
• PS-25 Normal and Self-Adjoint Operators
• PS-26 Unitary and Orthogonal Operators and Their Matrices
• PS-27 Orthogonal Projections and the Spectral Theorem
• PS-28 The Singular Value Decomposition and the Pseudoinverse