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

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Material type: Text

TextLanguage: English Series: UniversitextPublication details: New Delhi : Hindustan Book Agency, c2014.Description: 1 online resource (viii, 332 pages) : illustrationsISBN:

9783319041506 (electronic bk.)
3319041509 (electronic bk.)

Subject(s):

DDC classification:

512.943 HIA

Contents:

Fundamentals of operators and matrices -- Mappings and algebras -- Functional calculus and derivation -- Matrix monotone functions and convexity -- Matrix means and inequalities -- Majorization and singular values -- Some applications.

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.

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode
Project book	CUTN Central Library	512.943 HIA (Browse shelf(Opens below))	Checked out to Renuka Devi V (20019T)	31/01/2024	48869

Online version restricted to NUS staff and students only through NUSNET.

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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