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Sign determinacy of M-matrix minors

By Charles R. Johnson, D.D. Olesky, Brian Robertson and P. van den Driessche


AbstractWe show that if A is an M-matrix for which the length of the longest simple cycle in its associated undirected graph G(A) is at most 3, then every minor of A has determined sign (nonnegative or nonpositive), independent of the magnitudes of the matrix entries. Consequently, if A and B are M-matrices such that G(A) and G(B) are subgraphs of an undirected graph with longest simple cycle at most 3, then all principal minors of AB are nonnegative

Publisher: Published by Elsevier Inc.
Year: 1987
DOI identifier: 10.1016/0024-3795(87)90067-X
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