Hermitian quadratic eigenvalue problems of restricted rank |
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Authors: | Carlos Conca Heinrich Puschmann |
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Affiliation: | Departamento de Ingeniería Matemática Universidad de Chile, Santiago, Chile |
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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. 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 2r are nonreal occuring in possibly repeated conjugate pairs. |
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