{"product_id":"9780387002934","title":"CMS Books in Mathematics: Theory and Applications","description":"\u003ch1\u003eCMS Books in Mathematics: Theory and Applications\u003c\/h1\u003e \u003ch2\u003eBen-Israel, Adi; Greville, Thomas N.E.\u003c\/h2\u003e \u003cp\u003e1. 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2003-06-16\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780387002934\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/b97366\u003c\/p\u003e \u003cp\u003eDimensions: 234cm x156cm\u003c\/p\u003e \u003cp\u003ePages: 420\u003c\/p\u003e ","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":46541655638156,"sku":"9780387002934","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780387002934.jpg?v=1775744615","url":"https:\/\/lateknightbooks.com\/products\/9780387002934","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}