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Introduction to Matrix Analysis and Applications Fumio Hiai

Introduction to Matrix Analysis and Applications By Fumio Hiai

Introduction to Matrix Analysis and Applications by Fumio Hiai


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Summary

Several applications to quantum information are also included.

Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information.

Introduction to Matrix Analysis and Applications Summary

Introduction to Matrix Analysis and Applications by Fumio Hiai

Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis.

This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included.

Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.

Introduction to Matrix Analysis and Applications Reviews

"This volume, written in a clear and elegant style, provides a nice introduction to this actively studied area. It is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics." (Laszlo Kerchy, Acta Scientiarum Mathematicarum, Vol. 82 (1-2), 2016)

About Fumio Hiai

Fumio Hiai is an Emeritus Professor at the Graduate School of Information Science, Tohoku University, Sendai, Japan, whose research interests are operator theory, operator algebras and quantum probability. He published more than 95 papers and several books on various subjects of mathematics, including more than 20 papers on matrix analysis. His recent interest is also quantum information.

Table of Contents

Fundamentals of operators and matrices.- Mappings and algebras.- Functional calculus and derivation.- Matrix monotone functions and convexity.- Matrix means and inequalities.- Majorization and singular values.- Some applications.

Additional information

NGR9783319041490
9783319041490
3319041495
Introduction to Matrix Analysis and Applications by Fumio Hiai
New
Paperback
Springer International Publishing AG
2014-02-07
332
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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