Denis Serre: Matrices | Taschenbuch

Cover: 9781461427230 | Matrices | Theory and Applications | Denis Serre | Taschenbuch | XIV

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Beschreibung

In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: ¿ Dunford decomposition, ¿ tensor and exterior calculus, polynomial identities, ¿ regularity of eigenvalues for complex matrices, ¿ functional calculus and the Dunford¿Taylor formula, ¿ numerical range, ¿ Weyl's and von Neumann¿s inequalities, and ¿ Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.

Über den Autor

Denis Serre is Professor of Mathematics at École Normale Supérieure de Lyon and a former member of the Institut Universitaire de France. He is a member of numerous editorial boards and the author of "Systems of Conservation Laws" (Cambridge University Press 2000). With S. Benzoni-Gavage, he is the co-author of "Multi-Dimensional Hyperbolic Partial Differential Equations. First Order Systems and Applications" (Oxford University Press 2007). With S. Friedlander, he has co-edited four volumes of a "Handbook of Mathematical Fluid Dynamics" (Elsevier 2002--2007). The first edition of the present book is a translation of the original French edition, "Les Matrices: Théorie et Pratique", published by Dunod (2001).

Zusammenfassung

In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: . Dunford decomposition, . tensor and exterior calculus, polynomial identities, . regularity of eigenvalues for complex matrices, . functional calculus and the Dunford-Taylor formula, . numerical range, . Weyl's and von Neumann's inequalities, and . Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the Ecole Normale Supérieure de Lyon.

Inhaltsverzeichnis

Preface to the Second Edition.- Preface to the First Edition.- List of Symbols.- 1 Elementary Linear and Multilinear Algebra.- 2 What Are Matrices.- 3 Square Matrices.- 4 Tensor and Exterior Products.- 5 Matrices with Real or Complex Entries.- 6 Hermitian Matrices.- 7 Norms.- 8 Nonnegative Matrices.- 9 Matrices with Entries in a Principal Ideal Domain; Jordan Reduction.- 10 Exponential of a Matrix, Polar Decomposition, and Classical Groups.- 11 Matrix Factorizations and Their Applications.- 12 Iterative Methods for Linear Systems.- 13 Approximation of Eigenvalues.- References.- Index of Notation.- General Index.- Cited Names.-

Details

Erscheinungsjahr:	2012
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Graduate Texts in Mathematics
Inhalt:	xiv 289 S.
ISBN-13:	9781461427230
ISBN-10:	1461427231
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Serre, Denis
Auflage:	Softcover reprint of hardcover 2nd ed. 2010
Hersteller:	Springer New York Springer US, New York, N.Y. Graduate Texts in Mathematics
Maße:	235 x 155 x 17 mm
Von/Mit:	Denis Serre
Erscheinungsdatum:	25.12.2012
Gewicht:	0,464 kg

Artikel-ID: 106094450

Über den Autor

Zusammenfassung

In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: . Dunford decomposition, . tensor and exterior calculus, polynomial identities, . regularity of eigenvalues for complex matrices, . functional calculus and the Dunford-Taylor formula, . numerical range, . Weyl's and von Neumann's inequalities, and . Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the Ecole Normale Supérieure de Lyon.

Inhaltsverzeichnis

Details

Erscheinungsjahr:	2012
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Graduate Texts in Mathematics
Inhalt:	xiv 289 S.
ISBN-13:	9781461427230
ISBN-10:	1461427231
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Serre, Denis
Auflage:	Softcover reprint of hardcover 2nd ed. 2010
Hersteller:	Springer New York Springer US, New York, N.Y. Graduate Texts in Mathematics
Maße:	235 x 155 x 17 mm
Von/Mit:	Denis Serre
Erscheinungsdatum:	25.12.2012
Gewicht:	0,464 kg