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Positive Definite Matrices (Paperback)
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Positive Definite Matrices (Paperback)
Series: Princeton Series in Applied Mathematics
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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.
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