A new look at pencils of matrix valued functions (Q1344062)

Matrix pencils depending on a parameter and their canonical forms under equivalence are discussed. The authors give a survey of recent results for square pencils and extend these results to nonsquare pencils. Furthermore they partially extend the results for canonical forms of Hermitian pencils and give new canonical forms there, too. Based on these results, they obtain new existence and uniqueness theorems for differential-algebraic systems, which generalize the classical results of Weierstrass and Kronecker. The paper contains sections of constant pencils, local canonical form, global canonical form, existence and uniqueness of solutions of linear differential-algebraic equations, and numerical methods for general pencils.