Abstract
We determine all Hermitian -matrices for which every eigenvalue is in the interval [−2,2], for each d∈{−2,−7,−11,−15}. To do so, we generalise charged signed graphs to L-graphs for appropriate finite sets L, and classify all L-graphs satisfying the same eigenvalue constraints. We find that, as in the integer case, any such matrix/graph is contained in a maximal example with all eigenvalues ±2.
| Translated title of the contribution | Cyclotomic matrices and graphs over the ring of integers of some imaginary quadratic fields |
|---|---|
| Original language | English |
| Pages (from-to) | 523 - 545 |
| Number of pages | 23 |
| Journal | Journal of Algebra |
| Volume | 331 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Apr 2011 |