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Introduction to Matrix Analysis and Applications

  • Textbook
  • © 2014

Overview

Authors:
  1. Fumio Hiai

    1. Graduate School of Information Sciences, Tohoku University, Sendai, Japan

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  2. Dénes Petz

    1. Alfréd Rényi Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary

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    You can also search for this author in PubMed   Google Scholar

  • 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

Part of the book series: Universitext (UTX)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
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  2. Fundamentals of Operators and Matrices

    • Fumio Hiai, Dénes Petz
    Pages 1-53

  3. Mappings and Algebras

    • Fumio Hiai, Dénes Petz
    Pages 55-100

  4. Functional Calculus and Derivation

    • Fumio Hiai, Dénes Petz
    Pages 101-135

  5. Matrix Monotone Functions and Convexity

    • Fumio Hiai, Dénes Petz
    Pages 137-185

  6. Matrix Means and Inequalities

    • Fumio Hiai, Dénes Petz
    Pages 187-226

  7. Majorization and Singular Values

    • Fumio Hiai, Dénes Petz
    Pages 227-271

  8. Some Applications

    • Fumio Hiai, Dénes Petz
    Pages 273-322

  9. Back Matter

    Pages 323-332
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Keywords

About this book

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.

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)

Authors and Affiliations

  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan

    Fumio Hiai

  • Alfréd Rényi Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary

    Dénes Petz

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

  • DOI: https://doi.org/10.1007/978-3-319-04150-6

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Hindustan Book Agency 2014

  • Softcover ISBN: 978-3-319-04149-0Published: 20 February 2014

  • eBook ISBN: 978-3-319-04150-6Published: 06 February 2014

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: VIII, 332

  • Number of Illustrations: 3 b/w illustrations

  • Additional Information: Jointly published with Hindustan Book Agency, New Delhi, India

  • Topics: Linear and Multilinear Algebras, Matrix Theory

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