Introduction to Matrix Theory

Keeping the modest goal as a text book on matrix theory the approach here is straight forward and quite elementary. Using elementary row operations and Gram-Schmidt orthogonalization as basic tools the text develops characterization of equivalence and similarity and various factorizations such as rank factorization OR-factorization Schur triangularization Diagonalization of normal matrices Jordan decomposition singular value decomposition and polar decomposition. Along with Gauss-Jordan elimination for linear systems it also discusses best approximations and least squares solutions_ It includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix. The topics are dealt with in a lively manner. Each section of the book has exercises to reinforce the concepts; and problems have been added at the end of each chapter. Most of these problems are theoretical in nature and they do not fit into the running text linearly. Exercises and problems form an integral part of the book.Contents1. Matrix Operations 2. Systems of Linear Equations 3. Subspace and Dimension 4. Orthogonality 5. Eigenvalues and Eigenvectors 6. Canonical Forms 7. Norms of Matrices Short Bibliography Index.About the AuthorDr. Arindama Singh is currently Professor at the Department of Mathematics IIT Madras. He has 27 years of teaching and research experience out of which last 22 years is at IIT Madras. He has guided 5 Ph.D 4 M.Phil and 18 M.Sc. students so far. He has published 3 books 36 articles in refereed Journals and 10 papers in refereed conference proceedings. His areas of interest and research are Logic Theory of Computation and LinearAlgebra.