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Cover: 9781441918147 | Generalized Inverses | Theory and Applications | Greville (u. a.)
Bild: 9781441918147 | Generalized Inverses | Theory and Applications | Greville (u. a.)
Cover: 9781441918147 | Generalized Inverses | Theory and Applications | Greville (u. a.)
Bild: 9781441918147 | Generalized Inverses | Theory and Applications | Greville (u. a.)
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Generalized Inverses
Theory and Applications
Taschenbuch von Thomas N. E. Greville (u. a.)
Sprache: Englisch

74,89 €*

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Beschreibung
1. The Inverse of a Nonsingular Matrix It is well known that every nonsingular matrix A has a unique inverse, ?1 denoted by A , such that ?1 ?1 AA = A A =I, (1) where I is the identity matrix. Of the numerous properties of the inverse matrix, we mention a few. Thus, ?1 ?1 (A ) = A, T ?1 ?1 T (A ) =(A ) , ? ?1 ?1 ? (A ) =(A ) , ?1 ?1 ?1 (AB) = B A , T ? where A and A , respectively, denote the transpose and conjugate tra- pose of A. It will be recalled that a real or complex number ? is called an eigenvalue of a square matrix A, and a nonzero vector x is called an eigenvector of A corresponding to ?,if Ax = ?x. ?1 Another property of the inverse A is that its eigenvalues are the recip- cals of those of A. 2. Generalized Inverses of Matrices A matrix has an inverse only if it is square, and even then only if it is nonsingular or, in other words, if its columns (or rows) are linearly in- pendent. In recent years needs have been felt in numerous areas of applied mathematics for some kind of partial inverse of a matrix that is singular or even rectangular.
1. The Inverse of a Nonsingular Matrix It is well known that every nonsingular matrix A has a unique inverse, ?1 denoted by A , such that ?1 ?1 AA = A A =I, (1) where I is the identity matrix. Of the numerous properties of the inverse matrix, we mention a few. Thus, ?1 ?1 (A ) = A, T ?1 ?1 T (A ) =(A ) , ? ?1 ?1 ? (A ) =(A ) , ?1 ?1 ?1 (AB) = B A , T ? where A and A , respectively, denote the transpose and conjugate tra- pose of A. It will be recalled that a real or complex number ? is called an eigenvalue of a square matrix A, and a nonzero vector x is called an eigenvector of A corresponding to ?,if Ax = ?x. ?1 Another property of the inverse A is that its eigenvalues are the recip- cals of those of A. 2. Generalized Inverses of Matrices A matrix has an inverse only if it is square, and even then only if it is nonsingular or, in other words, if its columns (or rows) are linearly in- pendent. In recent years needs have been felt in numerous areas of applied mathematics for some kind of partial inverse of a matrix that is singular or even rectangular.
Über den Autor

Adi Ben-Israel is Professor of Operations Research, Business and Mathematics at Rutgers University, New Brunswick, NJ. Previously he was Professor of Applied Mathematics at the University of Delaware, Northwestern University, and the Technion-Israel Institute of Technology.

The late Thomas N.E. Greville was Professor of Mathematics, and a member of the US Army Mathematics Research Center at the University of Wisconsin, Madison, WI.

Zusammenfassung
The field of generalized inverses has grown much since the appearance
of the first edition in 1974, and is still growing. This book
accounts for these developments while maintaining the informal and
leisurely style of the first edition. New material has been added,
including a chapter on applications, an appendixo on the work of E.H.
Moore, new exercises and applications.
Inhaltsverzeichnis
* Glossary of notation * Introduction * Preliminaries * Existence and Construction of Generalized Inverses * Linear Systems and Characterization of Generalized Inverses * Minimal Properties of Generalized Inverses * Spectral Generalized Inverses * Generalized Inverses of Partitioned Matrices * A Spectral Theory for Rectangular Matrices * Computational Aspects of Generalized Inverses * Miscellaneous Applications * Generalized Inverses of Linear Operators between Hilbert Spaces * Appendix A: The Moore of the Moore-Penrose Inverse * Bibliography * Subject Index * Author Index
Details
Erscheinungsjahr: 2010
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: CMS Books in Mathematics
Inhalt: xvi
420 S.
1 s/w Illustr.
ISBN-13: 9781441918147
ISBN-10: 1441918140
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Greville, Thomas N. E.
Ben-Israel, Adi
Auflage: Softcover reprint of the original 2nd ed. 2003
Hersteller: Springer New York
Springer US, New York, N.Y.
CMS Books in Mathematics
Maße: 235 x 155 x 24 mm
Von/Mit: Thomas N. E. Greville (u. a.)
Erscheinungsdatum: 29.11.2010
Gewicht: 0,663 kg
Artikel-ID: 107253338
Über den Autor

Adi Ben-Israel is Professor of Operations Research, Business and Mathematics at Rutgers University, New Brunswick, NJ. Previously he was Professor of Applied Mathematics at the University of Delaware, Northwestern University, and the Technion-Israel Institute of Technology.

The late Thomas N.E. Greville was Professor of Mathematics, and a member of the US Army Mathematics Research Center at the University of Wisconsin, Madison, WI.

Zusammenfassung
The field of generalized inverses has grown much since the appearance
of the first edition in 1974, and is still growing. This book
accounts for these developments while maintaining the informal and
leisurely style of the first edition. New material has been added,
including a chapter on applications, an appendixo on the work of E.H.
Moore, new exercises and applications.
Inhaltsverzeichnis
* Glossary of notation * Introduction * Preliminaries * Existence and Construction of Generalized Inverses * Linear Systems and Characterization of Generalized Inverses * Minimal Properties of Generalized Inverses * Spectral Generalized Inverses * Generalized Inverses of Partitioned Matrices * A Spectral Theory for Rectangular Matrices * Computational Aspects of Generalized Inverses * Miscellaneous Applications * Generalized Inverses of Linear Operators between Hilbert Spaces * Appendix A: The Moore of the Moore-Penrose Inverse * Bibliography * Subject Index * Author Index
Details
Erscheinungsjahr: 2010
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: CMS Books in Mathematics
Inhalt: xvi
420 S.
1 s/w Illustr.
ISBN-13: 9781441918147
ISBN-10: 1441918140
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Greville, Thomas N. E.
Ben-Israel, Adi
Auflage: Softcover reprint of the original 2nd ed. 2003
Hersteller: Springer New York
Springer US, New York, N.Y.
CMS Books in Mathematics
Maße: 235 x 155 x 24 mm
Von/Mit: Thomas N. E. Greville (u. a.)
Erscheinungsdatum: 29.11.2010
Gewicht: 0,663 kg
Artikel-ID: 107253338
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