| Generalized Inverses: Theory and Applications Softcover Repri Edition Contributor(s): Ben-Israel, Adi (Author), Greville, Thomas N. E. (Author) |
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ISBN: 1441918140 ISBN-13: 9781441918147 Publisher: Springer OUR PRICE: $75.99 Product Type: Paperback - Other Formats Published: November 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Matrices - Medical - Mathematics | Algebra - Linear |
| Dewey: 512.943 |
| Series: CMS Books in Mathematics |
| Physical Information: 0.89" H x 6.14" W x 9.21" (1.35 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. |