Symmetric and skew-symmetric {0, ±1} - matrices with large determinants

• Main Authors: Greaves, Gary, Suda, Sho
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2020
• Subjects: Mathematics - Combinatorics; Science::Mathematics; D‐optimal Design; EW Matrix
• Online Access: https://hdl.handle.net/10356/144977
• Institution: Nanyang Technological University

We show that the existence of {±}-matrices having largest possible determinant is equivalent to the existence of certain tournament matrices. In particular, we prove a recent conjecture of Armario. We also show that large submatrices of conference matrices are determined by their spectrum.