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＜電子ブック＞
Introduction to Matrix Analysis and Applications / by Fumio Hiai, Dénes Petz
(Universitext. ISSN:21916675)

版	1st ed. 2014.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	VIII, 332 p. 3 illus : online resource
著者標目	*Hiai, Fumio author Petz, Dénes author SpringerLink (Online service)
件　名	LCSH:Algebras, Linear FREE:Linear Algebra
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-04150-6

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