 |
|
|
Item Details
| Title:
|
JORDAN CANONICAL FORM
THEORY AND PRACTICE |
| By: |
Steven H. Weintraub, Steven Krantz (Editor) |
| Format: |
Paperback |
| List price:
|
£40.95 |
|
We believe that this item is permanently unavailable, and so we cannot source
it.
|
|
|
|
|
|
| ISBN 10: |
1608452506 |
| ISBN 13: |
9781608452507 |
| Publisher: |
MORGAN & CLAYPOOL PUBLISHERS |
| Pub. date: |
1 October, 2009 |
| Series: |
Synthesis Lectures on Mathematics and Statistics |
| Pages: |
108 |
| 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. |
| Synopsis: |
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. |
| Illustrations: |
black & white illustrations |
| Publication: |
US |
| Imprint: |
Morgan & Claypool Publishers |
| Returns: |
Non-returnable |
|
|
|
 |
|
|
|
|
|
Little Worried Caterpillar (PB)
Little Green knows she''s about to make a big change - transformingfrom a caterpillar into a beautiful butterfly. Everyone is VERYexcited! But Little Green is VERY worried. What if being a butterflyisn''t as brilliant as everyone says?Join Little Green as she finds her own path ... with just a littlehelp from her friends.
|
|
All the Things We Carry PB
What can you carry?A pebble? A teddy? A bright red balloon? A painting you''ve made?A hope or a dream?This gorgeous, reassuring picture book celebrates all the preciousthings we can carry, from toys and treasures to love and hope. With comforting rhymes and fabulous illustrations, this is a warmhug of a picture book.
|
|
|
|