Theoretical Statistics and Mathematics Unit, ISI Delhi

On the Polars of Ordinally Weighted Unitarily Invariant Norms

by Govind S. Mudholkar and Yogendra P. Chaubey

Ordinally weighted unitarily invariant norms of matrices, or operators, are basically symmetric norms of their singular values weighted by an ordered set of weights. A trimmed version of these norms is obtained by considering only a few of the largest singular values. In this short note polars of these norms are characterized as in Mudholkar and Freimer (1985, Proc. Amer. Math. Soc., {\bf 95} 331-337). A simple expression for the weighted version of the Ky Fan $k-$norm is also obtained.

isid/ms/2014/13 [fulltext]

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