Based on lectures from Tohoku University and the Budapest University of Technology and Economics
Provides a strong emphasis to various areas of quantum theory, particularly quantum information theory
Covers classical topics and recent advances in the field
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.
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.
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.
"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.” (László Kérchy, Acta Scientiarum Mathematicarum, Vol. 82 (1-2), 2016)
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.
This book examines 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.
"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." (László Kérchy, Acta Scientiarum Mathematicarum, Vol. 82 (1-2), 2016)
Über den Autor
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.
Inhaltsverzeichnis
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.
Klappentext
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.
Based on lectures from Tohoku University and the Budapest University of Technology and Economics
Provides a strong emphasis to various areas of quantum theory, particularly quantum information theory
Covers classical topics and recent advances in the field
Includes supplementary material: sn.pub/extras
