A min–max theorem for complex symmetric matrices

Danciger, Jeffrey

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Publication date

January 2006

DOI

10.1016/j.laa.2005.06.020

Publisher

Elsevier Inc.

Abstract

AbstractWe optimize the form RextTx to obtain the singular values of a complex symmetric matrix T. We prove that for 0⩽k<n2,mincodimV=kmaxx∈V‖x‖=1RextTx=σ2k+1,whereT is an n×n complex symmetric matrix having singular values σ1⩾⋯⩾σn. We also show that the singular values missed in this theorem (i.e. σ2,σ4,…) are obtained by a similar optimization over real subspaces

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A min–max theorem for complex symmetric matrices

Abstract

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A min–max theorem for complex symmetric matrices

Abstract

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