Number-field cospectrality of symmetric integer matrices is characterized by discriminant and ramification conditions, and all cospectral mates over small totally real fields can be computed by a new algorithm.
Brown.Matrices over Commutative Rings
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Finding all cospectral mates over a number field
Number-field cospectrality of symmetric integer matrices is characterized by discriminant and ramification conditions, and all cospectral mates over small totally real fields can be computed by a new algorithm.