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ben-israel adi; greville thomas n.e. - generalized inverses
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Generalized Inverses Theory and Applications

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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 11/2010
Edizione: Softcover reprint of the original 2nd ed. 2003





Trama

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.




Sommario

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.




Autore

 

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.











Altre Informazioni

ISBN:

9781441918147

Condizione: Nuovo
Collana: CMS Books in Mathematics
Dimensioni: 235 x 155 mm
Formato: Brossura
Illustration Notes:XVI, 420 p.
Pagine Arabe: 420
Pagine Romane: xvi


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