Vol. 62, No. 2, 1976

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Subspaces of symmetric matrices containing matrices with a multiple first eigenvalue

Shmuel Friedland and Raphael Loewy

Vol. 62 (1976), No. 2, 389–399
Abstract

Let 𝒰 be an (r 1)(2nr + 2)2 dimensional subspace of n × n real valued symmetric matrices. Then 𝒰 contains a nonzero matrix whose greatest eigenvalue is at least of multiplicity r, if 2 r n 1. This bound is best possible. We apply this result to prove the Bohnenblust generalization of Calabi’s theorem. We extend these results to hermitian matrices.

Mathematical Subject Classification 2000
Primary: 15A57
Milestones
Received: 4 September 1975
Published: 1 February 1976
Authors
Shmuel Friedland
Mathematics, Statistics and Computer Science
University of Illinois at Chicago
SEO 322 (m/c 249)
851 South Morgan Street
Chicago IL 60607
United States
Raphael Loewy