Abstract
Jeter and Pye gave an example to show that Pang's conjecture, thatL 1 ⋂Q ⊂R 0, is false while Seetharama Gowda showed that the conjecture is true for symmetric matrices. It is known thatL 1-symmetric matrices are copositive matrices. Jeter and Pye as well as Seetharama Gowda raised the following question: Is it trueC 0 ⋂Q ⊂R 0? In this note we present an example of a copositive Q-matrix which is notR 0. The example is based on the following elementary proposition: LetA be a square matrix of ordern. SupposeR 1 =R 2 whereR i stands for theith row ofA. Further supposeA 11 andA 22 are Q-matrices whereA ii stands for the principal submatrix omitting theith row andith column fromA. ThenA is a Q-matrix.
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References
M.W. Jeter and W.C. Pye, “Some properties of Q-matrices,”Linear Algebra and its Applications 57 (1984) 169–180.
M.W. Jeter and W.C. Pye, “Some remarks on copositive Q-matrices and on a conjecture of Pang, Part I,”Industrial Mathematics 35 (1985) 75–80.
L.M. Kelly and L.T. Watson, “Q-matrices and spherical geometry,”Linear Algebra and its Applications 25 (1979) 175–189.
W.D. Morris, Jr., “Counterexamples to Q-matrix conjectures,”Linear Algebra and its Applications 111 (1988) 135–145.
J.S. Pang, “On Q-matrices,”Mathematical Programming 17 (1979) 243–247.
T. Parthasarathy and G. Ravindran, “The Jacobian matrix, global univalance and completely mixed games,”Mathematics of Operations Research 11 (1986) 663–671.
M. Seetharama Gowda, “On Q-matrices,”Mathematical Programming 49 (1990) 139–141.
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Murthy, G.S.R., Parthasarathy, T. & Ravindran, G. A copositive Q-matrix which is notR 0 . Mathematical Programming 61, 131–135 (1993). https://doi.org/10.1007/BF01582143
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DOI: https://doi.org/10.1007/BF01582143