Murthy, G. S. R. ; Parthasarathy, T. ; Ravindran, G.
(1993)
*A copositive Q-matrix which is not R _{0}*
Mathematical Programming, 61
(1-3).
pp. 131-135.
ISSN 0025-5610

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Official URL: http://www.springerlink.com/index/N245P23P528670RV...

Related URL: http://dx.doi.org/10.1007/BF01582143

## Abstract

Jeter and Pye gave an example to show that Pang's conjecture, that L_{1}∩Q ⊂ R_{0}, is false while Seetharama Gowda showed that the conjecture is true for symmetric matrices. It is known that L_{1}-symmetric matrices are copositive matrices. Jeter and Pye as well as Seetharama Gowda raised the following question: Is it true C_{0}∩Q ⊂ R_{0}? In this note we present an example of a copositive Q-matrix which is not R_{0}. The example is based on the following elementary proposition: Let A be a square matrix of order n. Suppose R_{1}=R_{2} where R_{i} stands for the ith row of A. Further suppose A_{11} and A_{22} are Q-matrices where A_{ii} stands for the principal submatrix omitting the ith row and ith column from A. Then A is a Q-matrix.

Item Type: | Article |
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Source: | Copyright of this article belongs to Springer. |

Keywords: | Linear Complementarity Problem; Copositive; Q-matrix |

ID Code: | 90939 |

Deposited On: | 15 May 2012 09:56 |

Last Modified: | 15 May 2012 09:56 |

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