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 A Farewell to Alms by Rajendra Bhatia
Cover of the book Complex Analysis by Rajendra Bhatia
Cover of the book A Savage War by Rajendra Bhatia
Cover of the book Impossible? by Rajendra Bhatia
Cover of the book On the Muslim Question by Rajendra Bhatia
Cover of the book The Book of Exodus by Rajendra Bhatia
Cover of the book The Last Freedom by Rajendra Bhatia
Cover of the book The Fourth Pig by Rajendra Bhatia
Cover of the book How Do You Find an Exoplanet? by Rajendra Bhatia
Cover of the book How the Idea of Religious Toleration Came to the West by Rajendra Bhatia
Cover of the book The Emergence of Organizations and Markets by Rajendra Bhatia
Cover of the book Planetary Climates by Rajendra Bhatia
Cover of the book The Impression of Influence by Rajendra Bhatia
Cover of the book A Culture of Growth by Rajendra Bhatia
Cover of the book The Story of Hebrew 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