Abstract
We consider a quadratic eigenvalue problem such that the second order term is a Hermitian matrix of rank r, the linear term is the identity matrix, and the constant term is an arbitrary Hermitian matrix A ∈ C n n . Of the n+ r solutions that this problem admits, we show at least n- r to be real and located in specific intervals defined by the eigenvalues of A, whence at most 2 r are nonreal occuring in possibly repeated conjugate pairs.
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