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Overview
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.
Editorials
Studia Universitatis Babes-Bolyai Mathematica
Written by an expert in the area, the book presents in an accessible manner a lot of important results from the realm of positive matrices and of their applications...The book can be used for graduate courses in linear algebra, or as supplementary material for courses in operator theory, and as a reference book by engineers and researchers working in the applied field of quantum information.— S. Cobzas
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There is no obvious competitor for Bhatia's book, due in part to its focus, but also because it contains some very recent material drawn from research articles. Beautifully written and intelligently organised, Positive Definite Matrices is a welcome addition to the literature. Readers who admired his Matrix Analysis will no doubt appreciate this latest book of Rajendra Bhatia.— Douglas Farenick
Zentralblatt MATH Database
This is an outstanding book. Its exposition is both concise and leisurely at the same time.— Jaspal Singh Aujla
Zentralblatt MATH
This is an outstanding book. Its exposition is both concise and leisurely at the same time.
— Jaspal Singh Aujla