On ray-nonsingular matrices

✍ Scribed by Hamid-Reza Fanaı̈

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 190 KB
• Volume: 376
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2003.06.012

✦ Synopsis

A complex matrix A is ray-nonsingular if det(X • A) / = 0 for every matrix X with positive entries. It is known that the order of a full ray-nonsingular matrix is at most 5 and examples of full n × n ray-nonsingular matrices for n = 2, 3, 4 exist. In this note, we describe a property of a special full 5 × 5 ray-nonsingular matrix, if such matrix exists, using the concept of an isolated set of transversals and we obtain a necessary condition for a complex matrix A to be ray-nonsingular. Moreover we give an example of a full 5 × 5 ray-pattern matrix that satisfies all three of the properties given by Lee et al. [Discrete Math. 216 (2000) 221-233]. The notion of Q-ray nonsingularity is also introduced.