Jordan Canonical Form : theory and practice /
By: Weintraub, Steven H.
Material type:
BookSeries: Synthesis lectures on mathematics and statistics: # 6.Publisher: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2009Description: 1 electronic text (x, 96 p. : ill.) : digital file.ISBN: 9781608452514 (electronic bk.).Uniform titles: Synthesis digital library of engineering and computer science. Subject(s): Jordan algebras | Algebras, Linear | EigenvaluesDDC classification: 512.24 Online resources: Abstract with links to resource Also available in print.| Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
E books
|
PK Kelkar Library, IIT Kanpur | Available | EBKE207 |
Mode of access: World Wide Web.
System requirements: Adobe Acrobat reader.
Part of: Synthesis digital library of engineering and computer science.
Series from website.
Includes index.
1. Fundamentals on vector spaces and linear transformations -- Bases and coordinates -- Linear transformations and matrices -- Some special matrices -- Polynomials in T and A -- Subspaces, complements, and invariant subspaces -- 2. The structure of a linear transformation -- Eigenvalues, eigenvectors, and generalized eigenvectors -- The minimum polynomial -- Reduction to BDBUTCD form -- The diagonalizable case -- Reduction to Jordan Canonical Form -- Exercises -- 3. An algorithm for Jordan Canonical Form and Jordan Basis -- The ESP of a linear transformation -- The algorithm for Jordan Canonical Form -- The algorithm for a Jordan Basis -- Examples -- Exercises -- A. Answers to odd-numbered exercises -- Notation -- Index.
Abstract freely available; full-text restricted to subscribers or individual document purchasers.
Compendex
INSPEC
Google scholar
Google book search
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 labelled eigenstructure picture (ESP) of A, determines P as well.We illustrate this algorithm with copious examples, and provide numerous exercises for the reader.
Also available in print.
Title from PDF t.p. (viewed on September 9, 2009).
There are no comments for this item.