No abstract

No abstract

No abstract

No abstract

Abstract. This paper provides necessary and sufficient conditions for a subspace of matrices to contain a dense set of matrices having distinct eigenvalues.A well-known and useful result in linear algebra is that matrices with distinct eigenvalues are dense in the set of n x n matrices. This result, however, does not hold for subspaces of matrices in general. For example, the subspace W=¡A:A= ° where a 6*1 contains no matrix with distinct eigenvalues. In this paper we give necessary and sufficient conditions for a subspace of matrices to contain a dense set of matrices having distinct eigenvalues. The result is then applied to subspaces of matrices determined by specified 0 patterns.