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Indian Institute of Technology Madras

Applied Linear Algebra

Indian Institute of Technology Madras and NPTEL via Swayam

Overview

Introduce the fundamentals of vector spaces, inner products, linear transformations, and eigenspaces to electrical engineering students.
INTENDED AUDIENCE :
Senior level Undergraduate and First year Postgraduate/PhDPREREQUISITES : Basic Calculus, Should have done a basic (or a first) course in Linear AlgebraINDUSTRIES SUPPORT :Communications, Artificial Intelligence, Analytics

Syllabus

COURSE LAYOUT

Week 1: Vectors and vector spacesWeek 2:Linear maps I: Definition, Spaces associated with a map, MatricesWeek 3:Linear maps II: Invertible linear maps, Elementary row/columnoperations, Solving linear equations, Quotient spaceWeek 4:Linear maps III: Four fundamental spaces, Rank of a matrix, Determinants, Change of basisWeek 5:Eigenvalues and eigenvectors of linear operatorsWeek 6: Applications of eigenvaluesWeek 7: Inner product spacesWeek 8:Projection and least squares
Week 9:Adjoint of linear maps and operators
Week 10:Self-adjoint and normal operatorsWeek 11:Positive operators, isometriesWeek 12:Polar and singular value decompositions

Taught by

Prof. Andrew Thangaraj

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