Jordan Canonical Form

Jordan Canonical Form
Theory and Practice

Steven H. Weintraub
ISBN: 9781608452507 | PDF ISBN: 9781608452514
Copyright © 2009 | 108 Pages | Publication Date: 01/01/2009

BEFORE YOU ORDER: You may have Academic or Corporate access to this title. Click here to find out: 10.2200/S00218ED1V01Y200908MAS006

Ordering Options: Paperback $30.00   E-book $24.00   Paperback & E-book Combo $37.50

Why pay full price? Members receive 15% off all orders.
Learn More Here

Read Our Digital Content License Agreement (pop-up)

Purchasing Options:


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 (?ESP) 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

Table of Contents

Jordan Canonical Form
Solving Systems of Linear Differential Equations
Background Results: Bases, Coordinates, and Matrices
Properties of the Complex Exponential

About the Author(s)

Steven H. Weintraub, Lehigh University

Reviews
Browse by Subject
ACM Books
IOP Concise Physics
0 items
LATEST NEWS

Newsletter
Note: Registered customers go to: Your Account to subscribe.

E-Mail Address:

Your Name: