SFB 303 Discussion Paper No. B-351

Author: Jain, S. K., S. K. Mitra, and Hans Joachim Werner

Title: Extensions of $\Gscr$-based Matrix Partial Orders
Abstract: We prove that a partial order $\preceq^{\Gscr}$ on matrix partial order $\preceq^{\Gscr}$ on $\R^ {m\times n}$ can always be extended to a $\Gscr$-based matrix partialorder $\preceq^{Gscr^*}$ such that $\Gscr^* ( A ) \ne\emtyset$ for all $A\in R^ ( {m\times n }$, thus answering an open Question [6]. It is further shown that $\Gscr6*$ should be semicmplete. And even if in a special situation this is possible and even if $\card\,\Gscr(A)\le 1$ for each $A$, then this does not mean that there also need be a semicomplete extension such that $\Gscr^*(A) is singleton for all $A$. In addition some other interesting results on matrix partial orders are given. For instance, a useful characterization for a semicomplete map to induce a partial order on the set of square matrices is derived.
Keywords: $\Gscr$-based matrix partial order, star order, minus
JEL-Classification-Number:: C69
Creation-Date: 1995
URL: ../1995/bonnsfb351.pdf

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