M-matrix products having positive principal minors |
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| Authors: | Charles R Johnson D D Olesky P van den Driessche |
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| Institution: | 1. Institute for Physical Science and Technology , University of Maryland , College Park, Maryland, 20742;2. Department of Computer Science , University of Victoria , B.C. V8W 2Y2, Victoria, Canada;3. Department of Mathematics , University of Victoria , B.C. V8W 2Y2, Victoria, Canada |
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| Abstract: | Sufficient conditions are given for powers and products of M-matrices to have all principal minors positive. Several of these conditions involve directed graphs of the matrices. In particular we show that if A and B are irreducible M-matrices which have longest simple circuit of length two with A+B having no simple circuit longer than three, then the product AB has all principal minors positive. |
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