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arXiv · 1202.1756

Small-span Hermitian matrices over quadratic integer rings

Gary Greaves
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Abstract

Building on the classification of all characteristic polynomials of integer symmetric matrices having small span (span less than 4), we obtain a classification of small-span polynomials that are the characteristic polynomial of a Hermitian matrix over some quadratic integer ring. Taking quadratic integer rings as our base, we obtain as characteristic polynomials some low-degree small-span polynomials that are not the characteristic (or minimal) polynomial of any integer symmetric matrix.

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Gary Greaves. 2013-06-10. Small-span Hermitian matrices over quadratic integer rings. https://doi.org/10.1090/s0025-5718-2014-02836-6

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