Transcription of Introduction to Matrix Analysis and Applications
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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.
statistics, engineering and economics may also find this book useful. Chapter 1 contains the basic subjects. We prefer the Hilbert space con-cepts, so complex numbers are used. Spectrum and eigenvalues are impor-tant. Determinant and trace are used later in several applications. The tensor product has symmetric and antisymmetric subspaces.
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