On the Existence of Matrices with Prescribed Height and Level Characteristics
نویسنده
چکیده
We detennine all possible relationa between the height (Weyr) characteristic and the level characteristic of an M-matrix. Under the assumption that the two characteristics have the same number of elements, we detennine the possible relations between the two characteristics for a wider class of matrices, which also contains the class of strictly triangular matrices over an arbitrary field. Given two sequences which satisfy the above condition, we conatruct a loople88 acyclic graph G with the following properly: Every matrix whose graph is G has its height characteristic equal to the first sequence and its level characteristic equal to the second. We give aeveral counterexamples to p088ible extensions of our results, and we raise some open problema.
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