Linear subspaces. Characteristic values and characteristic vectors. The formulas for matrix inversion. Matrix. Kronecker product and Kronecker sum. Invariant subspaces. Vector norms and matrix norms. Singular value decomposition. Generalized inversion. Quadratic forms and definite matrices. Matrix functions. Polynomial matrix. Lyapunov and Riccati matrix equation. Orthogonal transformations. Calculation of Shure and Jordan form. Conditioning and numerical stability. Rounding errors. Quadratic optimization