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Indian Institute of Technology Bombay

Basic Linear Algebra

Indian Institute of Technology Bombay and NPTEL via Swayam

Overview

Linear Algebr is a basic course for students intended to go for Engineering sudies and higher studies in Mathematics. We will cover the basic tools needed in these brances.
INTENDED AUDIENCE : B.Tech, B.Sc., M.Sc (maths) , BA/MA Economics/StatisticsPREREQUISITES : CoreINDUSTRY SUPPORT : Basic mathematics at school level undergraduate level

Syllabus

COURSE LAYOUT

Week 1: Matrices and Matrix operations, REF
Week 2: Linear systems, Gauss Elimination and Inverse of a matrix
Week 3: Rn; subspaces, linear independence, rank of a matrix
Week 4: Determinants, rank, inveribility
Week 5: Linear transformations,rank-nullity
Week 6: Inner product spaces, Gram-Schmidt process
Week 7: Eigenvalues and Eigenvectors
Week 8: Similarity, diagonalization and applications

TEACHING ASSISTANT
S. Venkitesh

S. Venkitesh is a final year Ph.D. student at IIT Bombay, with research interests in Combinatorics and Theoretical Computer Science, working with Prof. Srikanth Srinivasan. He has co-authored 3 research papers till date. His current research focuses on problems in Boolean function and circuit complexity, and theory and algorithms for linear codes, which have an inherent combinatorial/algebraic flavour. Two key methods often employed in such research are the polynomial method and the probabilistic method.He obtained his Masters’ degree in Mathematics from IIT Bombay (with Third rank) and Bachelors’ degree in Mathematics from University of Mumbai (with First rank). He has so far been a Teaching Assistant in 7 Mathematics courses of NPTEL and 10 courses at the Department of Mathematics, IIT Bombay. He also frequently accompanies the faculty of the Department of Mathematics, as a resource person for mathematics workshops at colleges in Mumbai.

Taught by

Prof. I.K.Rana

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