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Indian Institute of Technology Madras

Applied Linear Algebra

Indian Institute of Technology Madras and NPTEL via Swayam

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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


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

Click here to view the detailed syllabus

Taught by

Prof. Andrew Thangaraj



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