Abstract
Abstract : The paper gives conditions on a family of matrices which guarantee that some matrix in the family will have a multiple eigenvalue. In particular, the main theorem states exactly which dimensions admit k dimensional subspaces of matrices for which all nonzero elements have distinct eigenvalues. This question arises naturally in the theory of first order hyperbolic systems of partial differential equations; the main theorem, in this context, tells exactly for which integers n an n x n system in k space variables may be strictly hyperbolic. (Author)
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