Positive Definite Matrices (Princeton Series in Applied Mathematics) - Tapa dura

Bhatia, Rajendra

9780691129181: Positive Definite Matrices (Princeton Series in Applied Mathematics)

Tapa dura

ISBN 10: 0691129185 ISBN 13: 9780691129181

Editorial: Princeton University Press, 2007

Ver todas las copias de esta edici�n del ISBN

1 Usado

De EUR 201,00

0 Nuevo

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.

"Sinopsis" puede pertenecer a otra edici�n de este libro.

Acerca del autor

Rajendra Bhatia is Professor of Mathematics at the Indian Statistical Institute in New Delhi. He is the author of five books, including "Matrix Analysis".

De la contraportada

"This is a monograph for mathematicians interested in an important realm of matrix-analytic ideas. Like the author's distinguished book,Matrix Analysis, it will be a convenient and much-quoted reference source. There are many wonderful insights in a first-rate exposition of important ideas not easily extracted from other sources. The scholarship is impeccable."--Roger A. Horn, University of Utah

"I believe that every expert in matrix analysis can find something new in this book. Bhatia presents some important material in several topics related to positive definite matrices including positive linear maps, completely positive maps, matrix means, positive definite functions, and geometry of positive definite matrices. There are many beautiful results, useful techniques, and ingenious ideas here. Bhatia's writing style has always been concise, clear, and illuminating."--Xingzhi Zhan, East China Normal University