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Indian Institute of Science Bangalore

Linear Algebra

Indian Institute of Science Bangalore and NPTEL via Swayam

Overview

Linear Algebra is a foundational subject in Mathematics which is of fundamental importance in the development of almost every branch of Mathematics, Theoretical Physics and Computer Science. A good understanding of the subject is also crucial to the study of most Engineering disciplines and many problems in Social Sciences. Linear Algebra can be succinctly described as the study of Linear Transformations and its algebraic properties. This course is an introduction to Linear AlgebraINTENDED AUDIENCE : Undergraduate students in various universities.PREREQUISITES : NilINDUSTRY SUPPORT : Almost all engineering based companies

Syllabus

Week 1 : Vectors, vector spaces, span, linear independence, basesWeek 2 : Dimension, linear transformationsWeek 3 : Null spaces, range, coordinate basesWeek 4 : Matrix multiplication, Invertibility, IsomorphismsWeek 5 : Coordinate change, products and quotients of vector spaces, dualityWeek 6 : Review of elementary row operations, rank, determinantsWeek 7 : Eigenvalues, EigenvectorsWeek 8 : DiagonalizationWeek 9 : Characteristic polynomials, inner products and normsWeek 10 : Orthogonal bases, orthognalization, orthogonal complementsWeek 11 : Adjoints, normal and self-adjoint operatorsWeek 12 : Spectral theorem for normal and self-adjoint operators

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