Positive Definite Matrices

Nonfiction, Science & Nature, Mathematics, Matrices, Applied
Cover of the book Positive Definite Matrices by Rajendra Bhatia, Princeton University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Rajendra Bhatia ISBN: 9781400827787
Publisher: Princeton University Press Publication: January 10, 2009
Imprint: Princeton University Press Language: English
Author: Rajendra Bhatia
ISBN: 9781400827787
Publisher: Princeton University Press
Publication: January 10, 2009
Imprint: Princeton University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Princeton University Press

Cover of the book The Plum in the Golden Vase or, Chin P'ing Mei by Rajendra Bhatia
Cover of the book Attention Deficit Democracy by Rajendra Bhatia
Cover of the book Race in Another America by Rajendra Bhatia
Cover of the book Women in Western Political Thought by Rajendra Bhatia
Cover of the book School Lunch Politics by Rajendra Bhatia
Cover of the book Culture, 1922 by Rajendra Bhatia
Cover of the book The Gifts of Athena by Rajendra Bhatia
Cover of the book The Code of Capital by Rajendra Bhatia
Cover of the book Black Corona by Rajendra Bhatia
Cover of the book The Gamble: Random, or Romney? by Rajendra Bhatia
Cover of the book Provincializing Europe by Rajendra Bhatia
Cover of the book Masters of the Universe by Rajendra Bhatia
Cover of the book Terror in France by Rajendra Bhatia
Cover of the book Collected Works of C.G. Jung, Volume 13 by Rajendra Bhatia
Cover of the book Technology Differences over Space and Time by Rajendra Bhatia
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy