A copositive Q-matrix which is not R0

Murthy, G. S. R. ; Parthasarathy, T. ; Ravindran, G. (1993) A copositive Q-matrix which is not R0 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


Jeter and Pye gave an example to show that Pang's conjecture, that L1∩Q ⊂ R0, is false while Seetharama Gowda showed that the conjecture is true for symmetric matrices. It is known that L1-symmetric matrices are copositive matrices. Jeter and Pye as well as Seetharama Gowda raised the following question: Is it true C0∩Q ⊂ R0? In this note we present an example of a copositive Q-matrix which is not R0. The example is based on the following elementary proposition: Let A be a square matrix of order n. Suppose R1=R2 where Ri stands for the ith row of A. Further suppose A11 and A22 are Q-matrices where Aii stands for the principal submatrix omitting the ith row and ith column from A. Then A is a Q-matrix.

Item Type:Article
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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