Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
GSIS SELECTED LECTURES
Matrix Analysis: Matrix Monotone Functions, Matrix Means, and Majorization
Fumio HIAI
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Keywords: matrix, operator, inner product, norm, positive semidefinite, operator monotone, operator convex, divided difference, operator mean, eigenvalue, singular value, majorization, means
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Volume 16 (2010) Issue 2 Pages 139-248

DOI https://doi.org/10.4036/iis.2010.139
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Abstract

These lecture notes are concerned with several topics in matrix analysis covering the Löwner and Kraus theory on matrix/operator monotone and convex functions, the Kubo–Ando theory on operator means, spectral variation and majorization, and means for matrices. Matrix norm inequalities related to majorization and means for matrices are also discussed.

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© 2010 by the Graduate School of Information Sciences (GSIS), Tohoku University
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