Jordan Canonical Form: Theory and Practice. Steven Krantz, Steven Weintraub

Jordan Canonical Form: Theory and Practice



Download Jordan Canonical Form: Theory and Practice



Jordan Canonical Form: Theory and Practice Steven Krantz, Steven Weintraub ebook pdf
Publisher: Morgan & Claypool Publishers
Language: English
Page: 108
ISBN: 1608452506, 9781608452507

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



MORE EBOOKS:
Download Last Call: The Rise and Fall of Prohibition e book
Cliffsnotes Worldly Philosophers Notes (Cliffs Notes) cheap book







Tags: Jordan Canonical Form: Theory and Practice ebook pdf epub djvu mobi rar
Jordan Canonical Form: Theory and Practice pdf epub djvu free download
Download Jordan Canonical Form: Theory and Practice free ebook pdf epub
Jordan Canonical Form: Theory and Practice read online free book
Jordan Canonical Form: Theory and Practice cheap ebook for kindle and nook
Steven Krantz, Steven Weintraub ebooks and audio books
Jordan Canonical Form: Theory and Practice download pdf epub rar rapidshare mediafire fileserve 4shared torrent depositfiles scribd