A conjectured property of Hermitian pencils☆

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Abstract

If (A, B) is any pair of Hermitian matrices, the power of λ dividing det(λI−xA −yB) will be given by the number of basic singular summands in the pair. Contrary to conjecture, this power can be greater than one even when the pair is unitarily irreducible.

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This work was supported in part by the National Science Foundation, Grant MCS 8102967.

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