Cyclotomic matrices over real quadratic integer rings
arXiv:1201.6217 · doi:10.1016/j.laa.2012.06.003
Abstract
We classify all cyclotomic matrices over real quadratic integer rings and we show that this classification is the same as classifying cyclotomic matrices over the compositum all real quadratic integer rings. Moreover, we enumerate a related class of symmetric matrices; those matrices whose eigenvalues are contained inside the interval [-2,2] but whose characteristic polynomials are not in Z[x].
13 pages
References in corpus (4)
- A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices
- Cyclotomic matrices over the Eisenstein and Gaussian integers
- Cyclotomic Matrices and Graphs over the ring of integers of some imaginary quadratic fields
- Integer symmetric matrices having all their eigenvalues in the interval [-2,2]