Constructive characterization of Lipschitzian Q0-matrices

Murthy, G. S. R. ; Parthasarathy, T. ; Sriparna, B. (1997) Constructive characterization of Lipschitzian Q0-matrices Linear Algebra and its Applications, 252 (1-3). pp. 323-337. ISSN 0024-3795

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A matrix M∈Rn×n has property (∗∗) if M and all its principal pivotal transforms (PPTs) satisfy the property that the rows corresponding to the nonpositive diagonal entries are nonpositive. It has been shown that every Lipschitzian Q0-matrix satisfies property (∗∗). In this paper, it is shown that property (∗∗) is also sufficient for a Lipschitzian matrix to be in Q0. Property (∗∗) has several consequences. If A has this property, then A and all its PPTs must be completely Q0; further, for any q, the linear complementarity problem (q, A) can be processed by a simple principal pivoting method. It is shown that a negative matrix is an N-matrix if, and only if, it has property (∗∗); a matrix is a P-matrix if, and only if, it has property (∗∗) and its value is positive. Property (∗∗) also yields a nice decomposition structure of Lipschitzian matrices. This paper also studies properties of Lipschitzian matrices in general; for example, we show that the Lipschitzian property is inherited by all the principal submatrices.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:36621
Deposited On:11 Apr 2011 13:15
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