Jordan Canonical Form (Record no. 85125)
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fixed length control field | 03645nam a22005055i 4500 |
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control field | 978-3-031-02398-9 |
005 - DATE AND TIME OF LATEST TRANSACTION | |
control field | 20240730163919.0 |
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
fixed length control field | 220601s2009 sz | s |||| 0|eng d |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
ISBN | 9783031023989 |
-- | 978-3-031-02398-9 |
082 04 - CLASSIFICATION NUMBER | |
Call Number | 510 |
100 1# - AUTHOR NAME | |
Author | Weintraub, Steven H. |
245 10 - TITLE STATEMENT | |
Title | Jordan Canonical Form |
Sub Title | Theory and Practice / |
250 ## - EDITION STATEMENT | |
Edition statement | 1st ed. 2009. |
300 ## - PHYSICAL DESCRIPTION | |
Number of Pages | XI, 96 p. |
490 1# - SERIES STATEMENT | |
Series statement | Synthesis Lectures on Mathematics & Statistics, |
505 0# - FORMATTED CONTENTS NOTE | |
Remark 2 | Jordan Canonical Form -- Solving Systems of Linear Differential Equations -- Background Results: Bases, Coordinates, and Matrices -- Properties of the Complex Exponential. |
520 ## - SUMMARY, ETC. | |
Summary, etc | 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 (ℓESP) of A, determines P as well. We illustrate this algorithm with copious examples, and provide numerous exercises for the reader. Table of Contents: Fundamentals on Vector Spaces and Linear Transformations / The Structure of a Linear Transformation / An Algorithm for Jordan Canonical Form and Jordan Basis. |
856 40 - ELECTRONIC LOCATION AND ACCESS | |
Uniform Resource Identifier | https://doi.org/10.1007/978-3-031-02398-9 |
942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
Koha item type | eBooks |
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-- | Cham : |
-- | Springer International Publishing : |
-- | Imprint: Springer, |
-- | 2009. |
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-- | computer |
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-- | online resource |
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-- | text file |
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650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Mathematics. |
650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Statistics . |
650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Engineering mathematics. |
650 14 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Mathematics. |
650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Statistics. |
650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Engineering Mathematics. |
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
-- | 1938-1751 |
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-- | ZDB-2-SXSC |
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