On the Spectra of Striped Sign Patterns |
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| Authors: | J J McDonald D D Olesky M J Tsatsomeros P van den Driessche |
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| Institution: |
a Mathematics Department, Washington State University, Pullman, Washington 99164-3113, U.S.A..
b Department of Computer Science, University of Victoria, Victoria, British Columbia, Canada V8W 3P6.
c 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 -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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