| 书目名称 | Jordan Canonical Form | | 副标题 | Theory and Practice | | 编辑 | Steven H. Weintraub | | 视频video | | | 丛书名称 | Synthesis Lectures on Mathematics & Statistics | | 图书封面 |  | | 描述 | Jordan Canonical Form (JCF) is one of the most important, and useful, concepts in linear algebra. The JCF of a linear transformation, or of a matrix, encodes all of the structural information about that linear transformation, or matrix. This book is a careful development of JCF. After beginning with background material, we introduce Jordan Canonical Form and related notions: eigenvalues, (generalized) eigenvectors, and the characteristic and minimum polynomials. We decide the question of diagonalizability, and prove the Cayley-Hamilton theorem. Then we present a careful and complete proof of the fundamental theorem: Let V be a finite-dimensional vector space over the field of complex numbers C, and let T : V → V be a linear transformation. Then T has a Jordan Canonical Form. This theorem has an equivalent statement in terms of matrices: Let A be a square matrix with complex entries. Then A is similar to a matrix J in Jordan Canonical Form, i.e., there is an invertible matrix P and a matrix J in Jordan Canonical Form with A = PJP-1. We further present an algorithm to find P and J, assuming that one can factor the characteristic polynomial of A. In developing this algorithm we introd | | 出版日期 | Book 2009 | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-02398-9 | | isbn_softcover | 978-3-031-01270-9 | | isbn_ebook | 978-3-031-02398-9Series ISSN 1938-1743 Series E-ISSN 1938-1751 | | issn_series | 1938-1743 | | copyright | Springer Nature Switzerland AG 2009 |
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发表于 2025-3-21 19:41:20
