Introduction to matrix analysis and applications / Fumio Hiai and Denes Petz.
Material type:
TextSeries: UniversitextPublication details: New York : Springer, 2014.Description: viii, 332 p. ; illustrationsISBN: - 9783319041490
- 512.9434 23 H623
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 512.9434 H623 (Browse shelf(Opens below)) | Available | 135801 |
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| 512.9434 H432 Matrix theory for physicists | 512.9434 H434 Matrices for statistics | 512.9434 H468 Algebraic methods for toeplitzlike matrices and operators | 512.9434 H623 Introduction to matrix analysis and applications / | 512.9434 H623 Introduction to matrix analysis and applications / | 512.9434 H638 Applied group-theoretic and matrix methods | 512.9434 H719 Elementary matrix algebra |
Includes bibliographical references and index.
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--
Bibliography--
Index.
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.
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