Eigenvector matrices of symmetric tridiagonals

Summary A simple test is given for determining whether a given matrix is the eigenvector matrix of an (unknown) unreduced symmetric tridiagonal matrix. A list of known necessary conditions is also provided. A lower bound on the separation between eigenvalues of tridiagonals follows from our Theorem 3.Dedicated to Professor F.L. Bauer on the occasion of his 60th birthdayThe first author gratefully acknowledges support from ONR Contract N00014-76-C-0013