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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2009.
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| Edición: | 1st ed. 2009. |
| Colección: | Synthesis Lectures on Mathematics & Statistics,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 100 | 1 | |a Weintraub, Steven H. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Jordan Canonical Form |h [electronic resource] : |b Theory and Practice / |c by Steven H. Weintraub. |
| 250 | |a 1st ed. 2009. | ||
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| 300 | |a XI, 96 p. |b online resource. | ||
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| 490 | 1 | |a Synthesis Lectures on Mathematics & Statistics, |x 1938-1751 | |
| 505 | 0 | |a Jordan Canonical Form -- Solving Systems of Linear Differential Equations -- Background Results: Bases, Coordinates, and Matrices -- Properties of the Complex Exponential. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Mathematics. | |
| 650 | 0 | |a Statistics . | |
| 650 | 0 | |a Engineering mathematics. | |
| 650 | 1 | 4 | |a Mathematics. |
| 650 | 2 | 4 | |a Statistics. |
| 650 | 2 | 4 | |a Engineering Mathematics. |
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