منابع مشابه
Pseudo - tournament matrices , Brualdi - Li matrices and their new properties ∗
An n × n complex matrix A is h-pseudo-tournament if A + A∗ = hh∗ − I, where h is a complex, non-zero column vector. The class of h-pseudo-tournament matrices is a generalization of the well studied tournament-like matrices: h-hypertournament matrices, generalized tournament matrices and tournament matrices. In this paper we derive new spectral properties of an h-pseudo-tournament matrix. When t...
متن کاملEla Singular Values of Tournament Matrices
Upper and lower bounds on both the largest and smallest singular values of a tournament matrix M of order n are obtained. For most values of n, the matrices M for which equality holds are characterized.
متن کاملTournament Matrices with Extremal Spectral Properties
For a tournament matrix M of order n, we de ne its walk space, WM , to be SpanfM 1 : j = 0; . . . ; n 1g where 1 is the all ones vector. We show that the dimension of WM equals the number of eigenvalues of M whose real parts are greater than 1=2. We then focus on tournament matrices whose walk space has particularly simple structure, and characterize them in terms of their spectra. Speci cally,...
متن کاملA tournament approach to pattern avoiding matrices
We consider the following Turán-type problem: given a fixed tournament H, what is the least integer t = t(n,H) so that adding t edges to any n-vertex tournament, results in a digraph containing a copy of H. Similarly, what is the least integer t = t(Tn, H) so that adding t edges to the n-vertex transitive tournament, results in a digraph containing a copy of H. Besides proving several results o...
متن کاملPseudo-Tournament Matrices and Their Eigenvalues
Abstract. A tournament matrix and its corresponding directed graph both arise as a record of the outcomes of a round robin competition. An n × n complex matrix A is called h-pseudo-tournament if there exists a complex or real nonzero column vector h such that A+ A∗ = hh∗ − I . This class of matrices is a generalisation of well-studied tournament-like matrices such as h-hypertournament matrices,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1992
ISSN: 0024-3795
DOI: 10.1016/0024-3795(92)90384-m