Introduction to Matrix Analysis and Applications (Universitext) - Softcover

Hiai, Fumio; Petz, Dénes

Softcover

ISBN 10: 3319041495 ISBN 13: 9783319041490

Publisher: Springer, 2014

Synopsis

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.

About this title

About the Author

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.

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2014
• Language: English
• ISBN 10: 3319041495
• ISBN 13: 9783319041490
• Binding: Paperback
• Number of pages: 340