Relationships between the Completion Problems for Various Classes of Matrices
نویسنده
چکیده
where N = {1, . . . , n}. In this paper a pattern is assumed to include all diagonal positions. A symmetric pattern is a pattern with the property that (i, j) is in the pattern if and only if (j, i) is also in the pattern; symmetric patterns are also called positionally or combinatorially symmetric. An asymmetric pattern is a pattern with the property that if (i, j) is in the pattern, then (j, i) is not in the pattern. A partial matrix specifies the pattern if its specified entries are exactly those listed in the pattern. For a class X of real matrices, we say a pattern has Xcompletion if every partial X-matrix specifying the pattern can be completed to an X-matrix. The matrix completion problem (for patterns) for the class of Xmatrices is to determine which patterns have X-completion. Matrix completion problems have been studied for many classes of matrices, including positive definite matrices [6], P-matrices [11], [4], P0matrices [2], M-matrices [8], M0-matrices [9], inverse M-matrices [12], [7] and ______________
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تاریخ انتشار 2003