This definitive presentation of matrix theory is the work of one of America’s most significant contributors to this area. The first three chapters take matrix theory up to elementary divisors, proceeding to examinations of vector polynomials and singular matric polynomials. A discussion of compound matrices follows, succeeded by considerations of Hermitian, symmetric, and skew matrices, with a number of interesting proofs of properties. Subsequent chapters are devoted to commutative matrices, matrix functions, and the automorphic transformation of a bilinear form. The final chapter offers a masterly handling of linear associative algebras.