Spectrally arbitrary ray patterns |
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Authors: | Judith J McDonald |
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Institution: | a Mathematics Department, Washington State University, Pullman, WA 99164-3113, USA b Mathematics Department, Pacific Lutheran University, Tacoma, WA 98447, USA |
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Abstract: | An n×n ray pattern A is said to be spectrally arbitrary if for every monic nth degree polynomial f(x) with coefficients from C, there is a matrix in the pattern class of A such that its characteristic polynomial is f(x). In this article the authors extend the nilpotent-Jacobi method for sign patterns to ray patterns, establishing a means to show that an irreducible ray pattern and all its superpatterns are spectrally arbitrary. They use this method to establish that a particular family of n×n irreducible ray patterns with exactly 3n nonzeros is spectrally arbitrary. They then show that every n×n irreducible, spectrally arbitrary ray pattern has at least 3n-1 nonzeros. |
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Keywords: | 15A18 15A48 |
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