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.
"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
Rajendra Bhatia is Professor of Mathematics at the Indian Statistical Institute in New Delhi. He is the author of five books, including "Matrix Analysis".
Descrizione libro Paperback. Condizione libro: New. Softcover Book, New Condition, Fast Shipping. Ready in Stock. 1st Edition. [Please Read Carefully Before Buying], This Is An International Edition. Printed In Black and White. , Book Cover And ISBN No May Be Different From US Edition. Restricted Sales Disclaimer Wordings Not For Sales In USA And Canada May Be Printed On The Cover Of The Book. Standard Shipping 7-14 Business Days. Expedited Shiping 4-8 Business Days. ***WE DO NOT ENTERTAIN BULK ORDERS.*** The Books May Be Ship From Overseas For Inventory Purpose. Codice libro della libreria 467258
Descrizione libro Paperback. Condizione libro: New. New, Softcover International Edition, Printed in Black and White, Different ISBN, Same Content As US edition, Book Cover may be Different, in English Language. Codice libro della libreria 22465
Descrizione libro Princeton University Press. Hardcover. Condizione libro: New. 0691129185 New Condition. Codice libro della libreria NEW6.0354039
Descrizione libro Princeton University Press, 2007. Hardcover. Condizione libro: New. Codice libro della libreria P110691129185
Descrizione libro Princeton University Press, 2006. Hardcover. Condizione libro: New. Codice libro della libreria DADAX0691129185