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| 001 | 978-3-031-02398-9 | ||
| 003 | DE-He213 | ||
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| 008 | 220601s2009 sz | s |||| 0|eng d | ||
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_a9783031023989 _9978-3-031-02398-9 |
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_a10.1007/978-3-031-02398-9 _2doi |
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_aWeintraub, Steven H. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _981191 |
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| 245 | 1 | 0 |
_aJordan Canonical Form _h[electronic resource] : _bTheory and Practice / _cby Steven H. Weintraub. |
| 250 | _a1st ed. 2009. | ||
| 264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2009. |
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| 300 |
_aXI, 96 p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aSynthesis Lectures on Mathematics & Statistics, _x1938-1751 |
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| 505 | 0 | _aJordan Canonical Form -- Solving Systems of Linear Differential Equations -- Background Results: Bases, Coordinates, and Matrices -- Properties of the Complex Exponential. | |
| 520 | _aJordan 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. | ||
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_aMathematics. _911584 |
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_iPrinted edition: _z9783031012709 |
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_iPrinted edition: _z9783031035265 |
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_aSynthesis Lectures on Mathematics & Statistics, _x1938-1751 _981193 |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-02398-9 |
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