Small-span Hermitian matrices over quadratic integer rings

Details Small-span Hermitian matrices over quadratic integer rings Small-span Hermitian matrices over quadratic integer rings

2012-02-08

arxiv.org/abs/1202.1756v1

Mathematics

Number Theory

14 pages

Scientific paper

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

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