| 书目名称 | Generalized Inverses | | 副标题 | Theory and Applicati | | 编辑 | Adi Ben-Israel,Thomas N. E. Greville | | 视频video | | | 丛书名称 | CMS Books in Mathematics | | 图书封面 |  | | 描述 | 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. | | 出版日期 | Textbook 2003Latest edition | | 关键词 | Eigenvalue; Eigenvector; Hilbert space; Matrix; applied mathematics; field; matrices; spectral theory; matri | | 版次 | 2 | | doi | https://doi.org/10.1007/b97366 | | isbn_softcover | 978-1-4419-1814-7 | | isbn_ebook | 978-0-387-21634-8Series ISSN 1613-5237 Series E-ISSN 2197-4152 | | issn_series | 1613-5237 | | copyright | Springer Science+Business Media New York 2003 |
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发表于 2025-3-21 19:23:14
