Hermitian matrices of roots of unity and their characteristic polynomials

• المؤلفون الرئيسيون: Greaves, Gary Royden Watson, Woo, Chin Jian
• مؤلفون آخرون: School of Physical and Mathematical Sciences
• التنسيق: مقال
• اللغة: English
• منشور في: 2023
• الموضوعات: Science::Mathematics; Hermitian Matrices; Roots of Unity
• الوصول للمادة أونلاين: https://hdl.handle.net/10356/170926
• المؤسسة: Nanyang Technological University

We investigate spectral conditions on Hermitian matrices of roots of unity. Our main results are conjecturally sharp upper bounds on the number of residue classes of the characteristic polynomial of such matrices modulo ideals generated by powers of (1−ζ), where ζ is a root of unity. We also prove a generalisation of a classical result of Harary and Schwenk about a relation for traces of powers of a graph-adjacency matrix, which is a crucial ingredient for the proofs of our main results.