{"product_id":"9783031012709","title":"Synthesis Lectures on Mathematics \u0026 Statistics: Theory and Practice","description":"\u003ch1\u003eSynthesis Lectures on Mathematics \u0026amp; Statistics: Theory and Practice\u003c\/h1\u003e \u003ch2\u003eWeintraub, Steven H.\u003c\/h2\u003e \u003cp\u003eJordan 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\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2009-08-24\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783031012709\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-031-02398-9\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x191cm\u003c\/p\u003e \u003cp\u003ePages: 96\u003c\/p\u003e ","brand":"Morgan \u0026 Claypool","offers":[{"title":"Default Title","offer_id":46548032323724,"sku":"9783031012709","price":34.19,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783031012709.jpg?v=1776055653","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783031012709","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}