Basic operations -- Simultaneous linear equations -- Square matrices -- Matrix inversion -- Determinants -- Vectors -- Eigenvalues and eigenvectors -- Functions of matrices -- Canonical bases -- Similarity -- Inner products -- Norms -- Hermitian matrices -- Positive definite matrices -- Unitary transformations -- Quadratic forms and congruence -- Nonnegative matrices -- Patterned matrices -- Power methods for locating real eigenvalues --The QR algorithm -- Generalized inverses.