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Positive Definite Matrices

Af: Rajendra Bhatia Engelsk Paperback

Positive Definite Matrices

Af: Rajendra Bhatia Engelsk Paperback
Tjek vores konkurrenters priser

This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices.


Bhatia introduces several key topics in functional analysis, operator theory, harmonic analysis, and differential geometry--all built around the central theme of positive definite matrices. He discusses positive and completely positive linear maps, and presents major theorems with simple and direct proofs. He examines matrix means and their applications, and shows how to use positive definite functions to derive operator inequalities that he and others proved in recent years. He guides the reader through the differential geometry of the manifold of positive definite matrices, and explains recent work on the geometric mean of several matrices.



Positive Definite Matrices is an informative and useful reference book for mathematicians and other researchers and practitioners. The numerous exercises and notes at the end of each chapter also make it the ideal textbook for graduate-level courses.

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This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices.


Bhatia introduces several key topics in functional analysis, operator theory, harmonic analysis, and differential geometry--all built around the central theme of positive definite matrices. He discusses positive and completely positive linear maps, and presents major theorems with simple and direct proofs. He examines matrix means and their applications, and shows how to use positive definite functions to derive operator inequalities that he and others proved in recent years. He guides the reader through the differential geometry of the manifold of positive definite matrices, and explains recent work on the geometric mean of several matrices.



Positive Definite Matrices is an informative and useful reference book for mathematicians and other researchers and practitioners. The numerous exercises and notes at the end of each chapter also make it the ideal textbook for graduate-level courses.

Produktdetaljer
Sprog: Engelsk
Sider: 240
ISBN-13: 9780691168258
Indbinding: Paperback
Udgave:
ISBN-10: 0691168253
Udg. Dato: 1 sep 2015
Længde: 17mm
Bredde: 235mm
Højde: 157mm
Forlag: Princeton University Press
Oplagsdato: 1 sep 2015
Forfatter(e): Rajendra Bhatia
Forfatter(e) Rajendra Bhatia


Kategori Funktionsanalyse og transformation


ISBN-13 9780691168258


Sprog Engelsk


Indbinding Paperback


Sider 240


Udgave


Længde 17mm


Bredde 235mm


Højde 157mm


Udg. Dato 1 sep 2015


Oplagsdato 1 sep 2015


Forlag Princeton University Press

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