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Paper   IPM / M / 7264
School of Mathematics
  Title:   On ray-nonsingular matrices
  Author(s):  H. R. Fanai
  Status:   Published
  Journal: Linear Algebra Appl.
  Vol.:  376
  Year:  2004
  Pages:   125-134
  Supported by:  IPM
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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