Advertisement

© 2014

Introduction to Matrix Analysis and Applications

Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Fumio Hiai, Dénes Petz
    Pages 1-53
  3. Fumio Hiai, Dénes Petz
    Pages 55-100
  4. Fumio Hiai, Dénes Petz
    Pages 101-135
  5. Fumio Hiai, Dénes Petz
    Pages 137-185
  6. Fumio Hiai, Dénes Petz
    Pages 187-226
  7. Fumio Hiai, Dénes Petz
    Pages 227-271
  8. Fumio Hiai, Dénes Petz
    Pages 273-322
  9. Back Matter
    Pages 323-332

About this book

Introduction

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.

Keywords

Block Matrix Cramér–Rao Inqualtity Eigenvalue Entropy Functional Calculus Hilbert Space Jordan Canonical Form Majorization Matrix Analysis Matrix Mean Matrix Monotone Function Monotone Metric Optimal Quantum Measurement Positive Matrix Quantum Markov Triplets Symmetric Norm

Authors and affiliations

  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.Alfréd Rényi Institute of MathematicsBudapest University of Technology and EconomicsBudapestHungary

About the authors

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.

Bibliographic information

  • Book Title Introduction to Matrix Analysis and Applications
  • Authors Fumio Hiai
    Dénes Petz
  • Series Title Universitext
  • Series Abbreviated Title Universitext
  • DOI https://doi.org/10.1007/978-3-319-04150-6
  • Copyright Information Hindustan Book Agency 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-04149-0
  • eBook ISBN 978-3-319-04150-6
  • Series ISSN 0172-5939
  • Series E-ISSN 2191-6675
  • Edition Number 1
  • Number of Pages VIII, 332
  • Number of Illustrations 3 b/w illustrations, 0 illustrations in colour
  • Additional Information Jointly published with Hindustan Book Agency, New Delhi, India
  • Topics Linear and Multilinear Algebras, Matrix Theory
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking

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.” (László Kérchy, Acta Scientiarum Mathematicarum, Vol. 82 (1-2), 2016)