Linear Algebra: Vector and Inner Product Spaces

This book is a comprehensive guide to Linear Algebra and covers all the fundamental topics such as vector spaces, linear independence, basis, linear transformations, matrices, determinants, inner products, eigenvectors, bilinear forms, and canonical forms. It also introduces concepts such as fields, rings, group homomorphism, and binary operations early on, which gives students a solid foundation to understand the rest of the material. Unlike other books on Linear Algebra that are either too theory-oriented with fewer solved examples or too problem-oriented with less good quality theory, this book strikes a balance between the two. It provides easy-to-follow theorem proofs and a considerable number of worked examples with various levels of difficulty. The fundamentals of the subject are explained in a methodical and straightforward way. This book is aimed at undergraduate and graduate students of Mathematics and Engineering Mathematics who are studying Linear Algebra. It is also a useful resource for students preparing for exams in higher education competitions such as NET, GATE, lectureships, etc. The book includes some of the most recent and challenging questions from these exams.

I am currently employed with the School of Advanced Sciences - Mathematics Division, VIT Chennai, as an Assistant Professor (Sr.). I received my M.Sc. and D. Phil degrees from the University of Allahabad. I have published numerous papers in reputed journals. My main research interests include Topology, Wavelet Analysis, Application of Wavelet Methods to solve ODE & PDE. I am a Member of the Indian Mathematical Society. I have qualified for CSIR-JRF and GATE-Mathematics examinations. I have 10 years of teaching experience.