Title: Computing Stable Elgendecompositions of Matrix Pencils Classic Reprint
Publisher: Forgotten Books
Publication Date: 2018
Language: English
ISBN 10: 1332899013
ISBN 13: 9781332899012
Binding: PAP
Condition: New
Weight: 123 grams

About this title

Synopsis

Understand how small changes affect generalized eigenstructures in matrix pencils. This book explains a framework for computing stable decompositions of pencils A − λB, focusing on when the decomposition remains valid as the data varies within a tolerance. It links perturbation bounds to the block structure that reveals regular and singular parts, including left and right deflating subspaces.

In clear terms, the work introduces criteria to decide if a decomposition is stable, discusses the Kronecker Canonical Form, and shows how to bound how much the defining matrices P, Q, S, and T can change as A and B vary. It also connects theory to practical questions in controllability and observability, and describes how to verify stability using computable quantities.

Shows how perturbations influence the spectrum and deflating subspaces of A − λB.

Defines measurable bounds that determine when a decomposition remains valid across pencils in a family P(ε).

Relates stability to condition numbers of the deflating subspaces and to the sizes of finite and infinite eigenvalue blocks.

Applies to control system concepts like controllability and observability subspaces with a perturbation perspective.

Ideal for readers of advanced linear algebra and numerical analysis who want a rigorous treatment of stability in generalized eigenproblems and practical criteria for deciding when a decomposition is reliable.

"About this title" may belong to another edition of this title.

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