Jordan Canonical Form : theory and practice
The Resource Jordan Canonical Form : theory and practice Label
 Jordan Canonical Form : theory and practice
 Title remainder
 theory and practice
 Statement of responsibility
 Steven H. Weintraub
 Language
 eng
 Summary
 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 CayleyHamilton theorem. Then we present a careful and complete proof of the fundamental theorem: Let V be a finitedimensional 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 = PJP1.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
 Additional physical form
 Also available in print
 Cataloging source
 CaBNvSL
 Dewey number
 512.24
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA252.5
 LC item number
 .W455 2009
 Literary form
 non fiction
 Nature of contents

 dictionaries
 abstracts summaries
 Series statement
 Synthesis lectures on mathematics and statistics,
 Series volume
 # 6
 Target audience

 adult
 specialized
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