However, one thing we can say is that if and commute then will always have real eigenvalues, since the eigenvalues of all Hermitian operators are real. We mainly focus on inequalities bounding sums of r eigenvalues for C by sums of r eigenvalues for A with r eigenvalues for B, for some r less than n. ![]() 5 EIGENVALUES OF SUMS OF HERMITIAN MATRICES [after A. The scalar λ is called an eigenvalue of A, and any nonzero solution nx1 vector x G is an eigenvector. ![]() Eigenvalues of 2x2 hermitian matrix PAIGE McGill Univevsity Montreal, Quebec, Canada Communicated by Wallace Givens ABSTRACT It is a common experience that the perturbation, or even the omission, of some elements of a matrix often has negligible effect on some of the eigenvalues of the whole matrix.
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