This unique treatment of linear algebra establishes the central role of invariant subspaces in the analysis of linear transformation. Incorporating the newest developments in linear algebra stimulated by linear systems theory, it gives a comprehensive view of geometrical, algebraic, topological, and analytical properties of invariant subspaces, with an emphasis on applications to matrix polynomials, rational matrix functions, linear systems, and matrix quadratic equations. Also presented is an algebraic treatment of control and systems theories. Written by a world-famous expert, this text contains material not previously published, and includes numerous exercises.

A unified view of conformal invariants from the point of view of applications in geometric function theory and applications and quasiconformal mappings in the plane and in space.

This treatment of analysis on semigroups stresses the functional analytical and dynamical theory of continuous representations of semitopological semigroups. Topics covered include compact semitopological semigroups, invariant means and idempotent means on compact semitopological semigroups, affine compactifications, left multiplicatively continuous functions and weakly left continuous functions, compactifications of infinite direct products, and weakly almost periodic semigroups of Markov operators. Contains over 200 exercises, from simple applications and examples to further developments of the theory.