{"product_id":"generalized-inverses-theory-and-applications-cms-books-in-mathematics-0387002936","title":"Generalized Inverses: Theory and Applications (CMS Books in Mathematics)","description":"\u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 0387002936\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e Ben-Israel, Adi\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e New\u003c\/p\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","brand":"Mia Karts","offers":[{"title":"Default Title","offer_id":51824124887328,"sku":"NEW0387002936","price":108.08,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0980\/7426\/3840\/files\/51A_Wd_VEhL.jpg?v=1781208359","url":"https:\/\/miakarts.com\/products\/generalized-inverses-theory-and-applications-cms-books-in-mathematics-0387002936","provider":"Miakarts Books","version":"1.0","type":"link"}