Positive definite matrices /

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 d...

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Bibliographic Details
Main Author: Bhatia, Rajendra, 1952-
Format: Book
Published: Princeton, N.J. : Princeton University Press, [2007]
Series:Princeton series in applied mathematics
Table of Contents:
  • Positive Matrices
  • Characterizations
  • Some Basic Theorems
  • Block Matrices
  • Norm of the Schur Product
  • Monotonicity and Convexity
  • Supplementary Results and Exercises
  • Positive Linear Maps
  • Representations
  • Positive Maps
  • Some Basic Properties of Positive Maps
  • Some Applications
  • Three Questions
  • Positive Maps on Operator Systems
  • Supplementary Results and Exercises
  • Completely Positive Maps
  • Some Basic Theorems
  • Schwarz Inequalities
  • Positive Completions and Schur Products
  • The Numerical Radius
  • Supplementary Results and Exercises
  • Matrix Means
  • The Harmonic Mean and the Geometric Mean
  • Some Monotonicity and Convexity Theorems
  • Some Inequalities for Quantum Entropy
  • Furuta's Inequality
  • Supplementary Results and Exercises
  • Positive Definite Functions
  • Basic Properties
  • Loewner Matrices
  • Norm Inequalities for Means
  • Theorems of Herglotz and Bochner
  • Supplementary Results and Exercises
  • Geometry of Positive Matrices
  • The Riemannian Metric
  • The Metric Space P[ubscript]n
  • Center of Mass and Geometric Mean
  • Related Inequalities
  • Supplementary Results and Exercises.