This is a textbook on matrix theory and numerical computations involving matrices. The theory part treats vectors, matrices as operators, linear systems, invariant subspaces, \(\lambda\)-matrices, normal matrices, bilinear forms, matrix norms, functionals on Euclidean space, localization theorems, Toeplitz matrices, nonnegative matrices and matrix inequalities. The computation part deals with machine arithmetic, elementary matrices, orthogonalization, linear systems, over- and undertermined systems; inverse iteration, QR and QL and Lanczos algorithms for eigenvalues; iterative methods for linear systems, relaxation methods, ADI methods, Chebyshev iteration, c-g iteration. Though a textbook, it contains some recent material especially such emanating from Soviet researchers.