Research Communication | Open Access
Volume 2021 | Communication ID 273
Volume 2021 | Communication ID 273
| On the spectral properties of Tournament Matrices |
Brahim Chergui
Received |
Accepted |
Published |
February 01, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: A tournament matrix T is a (0, 1)-matrix that satisfies 〖T+T〗^t=J-I, where J is the all ones matrix and I is the identity matrix. Thus T has zero diagonal and t_ij=1 if and only if t_ij=0 for each i≠j. The directed graph associated with a tournament matrix is known as a tournament. S. Maybee and J. Pullman [5] extend several spectral properties of tournament matrices. In this paper, we study the eigenspaces of tournament matrices. These matrices (and their generalizations) appear in a variety of combinatorial applications (e.g., in biology, sociology, statistics, and networks).