Universitext

Introduction to Matrix Analysis and Applications

Authors: Hiai, Fumio, Petz, Denes

  • 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
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eBook $59.99
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  • ISBN 978-3-319-04150-6
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  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA
  • ISBN 978-3-319-04149-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
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About this Textbook

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 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.

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)


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Table of contents (7 chapters)

  • Fundamentals of Operators and Matrices

    Hiai, Fumio (et al.)

    Pages 1-53

  • Mappings and Algebras

    Hiai, Fumio (et al.)

    Pages 55-100

  • Functional Calculus and Derivation

    Hiai, Fumio (et al.)

    Pages 101-135

  • Matrix Monotone Functions and Convexity

    Hiai, Fumio (et al.)

    Pages 137-185

  • Matrix Means and Inequalities

    Hiai, Fumio (et al.)

    Pages 187-226

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-319-04150-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA
  • ISBN 978-3-319-04149-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Matrix Analysis and Applications
Authors
Series Title
Universitext
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Hindustan Book Agency
Distribution Rights
No distribution rights for India
eBook ISBN
978-3-319-04150-6
DOI
10.1007/978-3-319-04150-6
Softcover ISBN
978-3-319-04149-0
Series ISSN
0172-5939
Edition Number
1
Number of Pages
VIII, 332
Number of Illustrations and Tables
3 b/w illustrations
Additional Information
Jointly published with Hindustan Book Agency, New Delhi, India
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