Introduction to matrix analysis and applications / Fumio Hiai, Dénes Petz.

Format:

Book

Author/Creator:

Hiai, Fumio, 1948- author.

Petz, Dénes, 1953- author.

Series:

Universitext

Universitext, 0172-5939

Language:

English

Subjects (All):

Matrices.

Physical Description:

viii, 332 pages ; 24 cm.

Place of Publication:

Cham ; New York : Springer ; New Delhi : Hindustan Book Agency, [2014]

Summary:

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.

Contents:

1. Fundamentals of operators and matrices

2. Mappings and algebras

3. Functional calculus and derivation

4. Matrix monotone functions and convexity

5. Matrix means and inequalities

6. Majorization and singular values

7. Some applications.

Notes:

A co-publication withe Hindustan Book Agency, New Delhi, licensed for sale in all countries outside of India. Sold and distributed within India by the Hindustan Book Agency, P 19 Green Park Extension, New Delhi, India.

Includes bibliographical references (pages 323-326) and index.

ISBN:

3319041495

9783319041490

9380250606

9789380250601

OCLC:

874524546

Publisher Number:

Best.-Nr.: 86280149