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| Paper IPM / M / 7264 |
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| Abstract: | |
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A complex matrix A is ray-nonsingular if det(X°A) ≠ 0 for every matrix X with positive entries. It is known taht
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.
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