Modern Aspects of Linear Algebra

Introduction: Euclidean linear spaces Orthogonal and unitary linear transformations Orthogonal and unitary transformations. Singular values Matrices of operators in the Euclidean space: Unitary similar transformations. The Schur theorem Alternation theorems The Weyl inequalities Variational principles Resolvent and dichotomy of spectrum Quadratic forms in the spectrum dichotomy problem Matrix equations and projections The Hausdorff set of a matrix Application of spectral analysis. The most important algorithms: Matrix operators as models of differential operators Application of the theory of functions of complex variable Computational algorithms of spectral analysis Bibliography Index.