On orthogonal projectors induced by compact groups and Haar measures |
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Authors: | Marek Niezgoda |
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Institution: | Department of Applied Mathematics, Agricultural University in Lublin, PO Box 158, Akademicka 13, 20-950 Lublin, Poland |
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Abstract: | We study the difference of two orthogonal projectors induced by compact groups of linear operators acting on a vector space. An upper bound for the difference is derived using the Haar measures of the groups. A particular attention is paid to finite groups. Some applications are given for complex matrices and unitarily invariant norms. Majorization inequalities of Fan and Hoffmann and of Causey are rediscovered. |
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Keywords: | Orthogonal projector Compact group Haar measure Group majorization Singular values |
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