Subspaces of symmetric matrices containing matrices with a multiple first eigenvalue
Shmuel Friedland, Raphael Loewy · Pacific Journal of Mathematics · 1976
Let °\l be an (r -l)(2nr + 2)/2 dimensional subspace of rc x 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 CalabFs theorem.We extend these results to hermitian matrices.