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Introduction to Matrix Analysis and Applications

Introduction to MatrixAnalysis and ApplicationsFumio Hiai and D enes PetzGraduate School of Information SciencesTohoku University, Aoba-ku, Sendai, 980-8579, JapanE-mail: ed R enyi Institute of MathematicsRe altanoda utca 13-15, H-1364 Budapest, HungaryE-mail: part of the material of this book is based on the lectures of the authorsin the Graduate School of Information Sciences of Tohoku University andin the Budapest University of Technology and Economics. The aim of thelectures was to explain certain important topics on Matrix Analysis from thepoint of view of functional Analysis . The concept of Hilbert space appearsmany times, but only finite-dimensional spaces are used. The book treatssome aspects of Analysis related to matrices including such topics asmatrixmonotone functions, Matrix means, majorization, entropies, quantum Markovtriplets.

Fundamentals of operators and matrices A linear mapping is essentially matrix if the vector space is finite dimensional. In this book the vector space is typically finite dimensional complex Hilbert-space. 1.1 Basics on matrices For n,m∈ N, Mn×m = Mn×m(C) denotes the space of all n× mcomplex matrices.

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