Introduction to Matrix Analysis and Applications

  • Fumio Hiai
  • Dénes Petz

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


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.


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

  • Fumio Hiai
    • 1
  • Dénes Petz
    • 2
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.Alfréd Rényi Institute of MathematicsBudapest University of Technology and EconomicsBudapestHungary

Bibliographic information

  • DOI
  • Copyright Information Hindustan Book Agency 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-04149-0
  • Online ISBN 978-3-319-04150-6
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book