A copositive Q-matrix which is notR
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| Authors: | G S R Murthy T Parthasarathy G Ravindran |
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| Institution: | (1) Indian Statistical Institute, Madras, India;(2) Indian Statistical Institute, Delhi Centre, 7, S.J.S. Sansanwal Marg, 110016 New Delhi, India;(3) University of Hyderabad, India |
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| 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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| Keywords: | Linear complementarity problem copositive Q-matrix |
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