On the Spectra of Striped Sign Patterns |
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Authors: | JJ McDonald DD Olesky MJ Tsatsomeros P van den Driessche |
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Institution: | 1. Mathematics Department , Washington State University , Pullman, Washington, 99164-3113, U.S.A.;2. Department of Computer Science , University of Victoria , Victoria, British Columbia, Canada , V8W 3P6;3. Department of Mathematics and Statistics , University of Victoria , Victoria, British Columbia, Canada , V8W 3P4 |
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Abstract: | Sign patterns consisting of some positive and some negative columns, with at least one of each kind, are shown to allow any self-conjugate spectrum, and thus to allow any inertia. In the case of the n × n sign pattern with all columns positive, given any self-conjugate multiset consisting of n m 1 complex numbers supplemented by a sufficiently large positive number, it is shown how to construct a positive normal matrix whose spectrum is this multiset. Thus, the positive sign pattern allows any inertia with at least one positive eigenvalue. |
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Keywords: | Spectrum Nonnegative Matrix Sign Pattern Soules Matrix Inertia |
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