{"product_id":"jordan-canonical-form-theory-and-practice-9783031012709","title":"Jordan Canonical Form: Theory and Practice","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\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\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eJordan Canonical Form.- Solving Systems of Linear Differential Equations.- Background Results: Bases, Coordinates, and Matrices.- Properties of the Complex Exponential.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":51742890721623,"sku":"9783031012709","price":25.19,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031012709.jpg?v=1758387159","url":"https:\/\/bookcurl.com\/products\/jordan-canonical-form-theory-and-practice-9783031012709","provider":"Book Curl","version":"1.0","type":"link"}