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Sufficient conditions for the solvability of an algebraic inverse eigenvalue problem. (English) Zbl 0827.15005

Some sufficient conditions are derived for the existence of real numbers \(c_1, \ldots, c_n\) such that \(A + \sum^n_{t = 1} c_t A_t\) has a prescribed set of eigenvalues, where \(A\), \(A_1, \ldots, A_n\) are given \(n \times n\) Hermitian matrices. Examples are given which satisfy these conditions but which do not satisfy some previously known sufficient conditions for the existence of solutions.

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
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References:

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