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Square matrix
About: Square matrix is a research topic. Over the lifetime, 5000 publications have been published within this topic receiving 92428 citations.
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TL;DR: This paper forms this problem as a linear complementarity problem with a square matrixM, a formulation which is different from a similar formulation given earlier by Lemke, and shows that the class of vertical block matrices which Cottle and Dantzig's algorithm can process is the same as theclass of equivalent square matrices in Lemke's algorithm.
Abstract: Given a vertical block matrixA, we consider in this paper the generalized linear complementarity problem VLCP(q, A) introduced by Cottle and Dantzig. We formulate this problem as a linear complementarity problem with a square matrixM, a formulation which is different from a similar formulation given earlier by Lemke. Our formulation helps in extending many well-known results in linear complementarity to the generalized linear complementarity problem. We also show that the class of vertical block matrices which Cottle and Dantzig's algorithm can process is the same as the class of equivalent square matrices which Lemke's algorithm can process. We also present some degree-theoretic results on a vertical block matrix.
43 citations
TL;DR: A new right-preconditioning process similar to the one presented by Neumaier in 1987 but in the more general context of the inner and outer estimations of linear AEsolution sets is presented, presented in the form of two new auxiliary interval equations.
Abstract: Aright-preconditioning process for linear interval systems has been presented by Neumaier in 1987. It allows the construction of an outer estimate of the united solution set of a square linear interval system in the form of a parallelepiped. The denomination “right-preconditioning” is used to describe the preconditioning processes which involve the matrix product AC in contrast to the (usual) left-preconditioning processes which involve the matrix product AC, where A and C are respectively the interval matrix of the studied linear interval system and the preconditioning matrix.
43 citations
TL;DR: In this paper, Hartwig and Spindelbock demonstrate that Corollary 6 in [R.E. Hartwig, K. Köpcke] provides a powerful tool to investigate square matrices with complex entries.
43 citations
TL;DR: In this paper, it was proved that the iterative methods of [1] are convergent to a fixed inner inverse of the matrix which is the Moore-Penrose inverse.
43 citations
TL;DR: In this article, it was shown that basic descriptive quantities, such as the stationary vector and mean first-passage matrix, can be calculated using any one of a class of fundamental matrices.
43 citations