{"product_id":"jordan-canonical-form-steven-h-weintraub-9783031012709","title":"Jordan Canonical Form: Theory and Practice","description":"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 introduce the eigenstructure picture (ESP) of a matrix, a pictorial representation that makes JCF clear. The ESP of A determines J, and a refinement, the labeled eigenstructure picture (ℓESP) of A, determines P as well. We illustrate this algorithm with copious examples, and provide numerous exercises for the reader. Table of Contents: Fundamentals on Vector Spaces and Linear Transformations \/ The Structure of a Linear Transformation \/ An Algorithm for Jordan Canonical Form and Jordan Basis\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Steven H. Weintraub\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3031012704\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783031012709\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 08\/24\/2009\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 96\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.45lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.25h x 7.50w x 0.23d","brand":"Steven H. Weintraub","offers":[{"title":"Paperback","offer_id":44123341783295,"sku":"9783031012709","price":37.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_6351e7f8-b2cc-4224-a03b-0fc9f464adce.jpg?v=1687430336","url":"https:\/\/www.whiterainbookhouse.com\/products\/jordan-canonical-form-steven-h-weintraub-9783031012709","provider":"WR Book House","version":"1.0","type":"link"}