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This book is dedicated to relatively recent results in linear algebra with indefinite inner product. It also includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications have been developed in the last fifty years, and all of them are based on linear algebra in spaces with indefinite inner product. The latter forms a new more or less independent branch of linear algebra and we gave it the name of indefinite linear algebra. This new subject in linear algebra is presented following the lines and principles of a standard linear algebra course. This book has the structure of a graduate text in which chapters of advanced linear algebra form the core. This together with the many significant applications and accessible style will make it widely useful for engineers, scientists and mathematicians alike.

Operator theory --- lineaire algebra --- analyse (wiskunde)

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This book is dedicated to relatively recent results in linear algebra with indefinite inner product. It also includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications have been developed in the last fifty years, and all of them are based on linear algebra in spaces with indefinite inner product. The latter forms a new more or less independent branch of linear algebra and we gave it the name of indefinite linear algebra. This new subject in linear algebra is presented following the lines and principles of a standard linear algebra course. This book has the structure of a graduate text in which chapters of advanced linear algebra form the core. This together with the many significant applications and accessible style will make it widely useful for engineers, scientists and mathematicians alike.

Operator theory --- lineaire algebra --- analyse (wiskunde)

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Operator theory --- Functional analysis --- analyse (wiskunde) --- functies (wiskunde)

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Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces. Key Features- Provides an ideal transition between introductory math courses and advanced graduate study in applied math

Functional analysis. --- Operator theory. --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations

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The Schur complement plays an important role in matrix analysis, statistics, numerical analysis, and many other areas of mathematics and its applications. This book describes the Schur complement as a rich and basic tool in mathematical research and applications and discusses many significant results that illustrate its power and fertility. The eight chapters of the book cover themes and variations on the Schur complement, including its historical development, basic properties, eigenvalue and singular value inequalities, matrix inequalities in both finite and infinite dimensional settings, closure properties, and applications in statistics, probability, and numerical analysis. The chapters need not be read in order, and the reader should feel free to browse freely through topics of interest. Although the book is primarily intended to serve as a research reference, it will also be useful for graduate and advanced undergraduate courses in mathematics, applied mathematics, and statistics. The contributing authors' exposition makes most of the material accessible to readers with a sound foundation in linear algebra. The book, edited by Fuzhen Zhang, was written by several distinguished mathematicians: T. Ando (Hokkaido University, Japan), C. Brezinski (Université des Sciences et Technologies de Lille, France), R. Horn (University of Utah, Salt Lake City, U.S.A.), C. Johnson (College of William and Mary, Williamsburg, U.S.A.), J.-Z. Liu (Xiangtang University, China), S. Puntanen (University of Tampere, Finland), R. Smith (University of Tennessee, Chattanooga, USA), and G.P.H. Steyn (McGill University, Canada). Fuzhen Zhang is a professor of Nova Southeastern University, Fort Lauderdale, U.S.A., and a guest professor of Shenyang Normal University, Shenyang, China. Audience This book is intended for researchers in linear algebra, matrix analysis, numerical analysis, and statistics.

Statistical science --- Algebra --- Operator theory --- Numerical analysis --- algebra --- analyse (wiskunde) --- matrices --- numerieke analyse --- statistisch onderzoek