Hermitian matrices of roots of unity and their characteristic polynomials

• Main Authors: Greaves, Gary Royden Watson, Woo, Chin Jian
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2023
• Subjects: Science::Mathematics; Hermitian Matrices; Roots of Unity
• Online Access: https://hdl.handle.net/10356/170926
• Institution: 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...