Indefinite Linear Algebra and Applications (Paperback, 2005 ed.)

Thefollowing topics ofmathematical analysishavebeen developed in the last?fty years: thetheoryoflinearcanonicaldi?erentialequationswithperiodicHamilto- ans, the theory of matrix polynomials with selfadjoint coe?cients, linear di?er- tial and di?erence equations of higher order with selfadjoint constant coe?cients, andalgebraicRiccati equations.All of these theories, and others, arebased on r- atively recent results of linear algebra in spaces with an inde?nite inner product, i.e., linear algebra in which the usual positive de?nite inner product is replaced by an inde?nite one. More concisely, we call this subject inde?nite linear algebra. This book has the structureof a graduatetext in which chaptersof advanced linear algebra form the core. The development of our topics follows the lines of a usual linear algebra course. However, chapters giving comprehensive treatments of di?erential and di?erence equations, matrix polynomials and Riccati equations are interwoven as the necessary techniques are developed. The main source of material is our earlier monograph in this ?eld: Matrices and Inde?nite Scalar Products, 40]. The present book di?ers in objectives and material.Somechaptershavebeenexcluded, othershavebeenadded, andexercises have been added to all chapters. An appendix is also included. This may serve as a summary and refresher on standard results as well as a source for some less familiar material from linear algebra with a de?nite inner product. The theory developed here has become an essential part of linear algebra. This, together with the many signi?cant areas of application, and the accessible style, make this book useful for engineers, scientists and mathematicians al