Jordan Canonical Form (Record no. 85125)
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| 000 -LEADER | |
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| fixed length control field | 03645nam a22005055i 4500 |
| 001 - CONTROL NUMBER | |
| 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 |
| 264 #1 - | |
| -- | Cham : |
| -- | Springer International Publishing : |
| -- | Imprint: Springer, |
| -- | 2009. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 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 |
| 912 ## - | |
| -- | ZDB-2-SXSC |
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