Synopsis The book presents a systematic development of matrix theory and methods. It treats the theory of finite-dimensional vector spaces in detail and then uses vector space methods to prove results on matrices. Several simple techniques like rank-factorization, rank-cancellation laws, g-inverses and hermite canonical form are clearly explained and used to simplify several proofs. Also presented are comprehensive accounts of the square root method, the Compact Gauss-Doolittle (LU) method and the singular value decomposition. The computational procedures are presented as algorithms which can easily be converted into computer programs. Numerous examples illustrating the concepts, results and procedures are included. Also included are a large number of exercises with hints for solutions. The treatment of some topics like span and linear independence and proofs of some results like those on square-root method are simplified in the current edition. A discussion of the general equation of the second degree in two variables is also included. With its comprehensive coverage, the book meets the requirements of advanced undergraduate students of mathematics and statistics as well as students of engineering.