Please note: In order to keep Hive up to date and provide users with the best features, we are no longer able to fully support Internet Explorer. The site is still available to you, however some sections of the site may appear broken. We would encourage you to move to a more modern browser like Firefox, Edge or Chrome in order to experience the site fully.

Supporting your high street Find out how »
Jordan Canonical Form : Theory and Practice, Paperback / softback Book

Jordan Canonical Form : Theory and Practice Paperback / softback

Part of the Synthesis Lectures on Mathematics and Statistics series

Paperback / softback

Item not Available

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 (?ESP) of A, determines P as well.

We illustrate this algorithm with copious examples, and provide numerous exercises for the reader.

Information

Other Formats

£40.95

Item not Available
Item not Available
Sign in to add to wishlist
 
Free Home Delivery

on all orders

 
Pick up orders

from local bookshops

Information