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Jordan Canonical Form theory and practice /

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...

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Bibliographic Details
Main Author: Weintraub, Steven H.
Format: Electronic
Language:English
Published: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2009.
Series:Synthesis lectures on mathematics and statistics (Online), # 6.
Subjects:
Jordan algebras.
Algebras, Linear.
Eigenvalues.
Online Access:Abstract with links to full text
Table of Contents:
  • 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.

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