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Jordan Canonical Form: Theory and Practice (Synthesis Lectures on Mathematics and Statistics) - Softcover
Inhaltsangabe
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
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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
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- VerlagMorgan & Claypool Publishers
- Erscheinungsdatum2009
- ISBN 10 1608452506
- ISBN 13 9781608452507
- EinbandTapa blanda
- SpracheEnglisch
- Anzahl der Seiten108
- Kontakt zum HerstellerNicht verfügbar
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Jordan Canonical Form Theory and Practice - Synthesis Lectures on Mathematics and Statistics
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Softcover. Zustand: Sehr gut. Weintraub Steven H. Jordan Canonical Form Theory and Practice - Synthesis Lectures on Mathematics and Statistics SC - 19 x 23 cm - Verlag: Morgan & Claypool - 2009 - ISBN: 9781608452507 - 96 Seiten - Englisch Klappentext: 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 ofJCE 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 thefield ofcomplex numbers C, and let T: V --> 5 V be a linear transformation. Then T has a Jordan Canonical Form. This theorem has an equivalent statement in terms of matrices: LetA be a square matrix with complex entries. Then A is similar to a matrixJ in Jordan Canonical Form, i.e., there is an invertible matrix P a matrixJ in Jordan Canonical Form withA pp-l. We further present an algorithm to find P andJ, assuming that one can factor the characteristic polynomial ofA. 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 VESP) ofA, determines P as well. We illustrate this algorithm With copious examples, and provide numerous exercises for the reader. Zustand: SEHR GUT! Einband mit gnaz leichten Gebrauchsspuren, innen sehr sauber. Size: 19 x 23 Cm. Buch. Artikel-Nr. 035566
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