Minimum Rank Problems
نویسنده
چکیده
A graph describes the zero-nonzero pattern of a family of matrices, with the type of graph (undirected or directed, simple or allowing loops) determining what type of matrices (symmetric or not necessarily symmetric, diagonal entries free or constrained) are described by the graph. The minimum rank problem of the graph is to determine the minimum among the ranks of the matrices in this family; the determination of maximum nullity is equivalent. This problem has been solved for simple trees [11, 9], trees allowing loops [5], and directed trees allowing loops [2]. We survey these results from a unified perspective and solve the minimum rank problem for simple directed trees.
منابع مشابه
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تاریخ انتشار 2009