| Generalized Inverses: Theory and Applications 2003 Edition Contributor(s): Ben-Israel, Adi (Author), Greville, Thomas N. E. (Author) |
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ISBN: 0387002936 ISBN-13: 9780387002934 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: June 2003 Annotation: 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 appendix on the work of E.H. Moore, new exercises and applications. |
| Additional Information |
| BISAC Categories: - Mathematics | Matrices - Medical |
| Dewey: 512.943 |
| LCCN: 2002044506 |
| Series: CMS Books in Mathematics |
| Physical Information: 0.96" H x 6.1" W x 9.68" (1.63 lbs) 420 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |