Sign patterns that require real,nonreal or pure imaginary eigenvalues |
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| Authors: | Carolyn A Eschenbach Charles R Johnson |
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| Institution: | 1. Department of Mathematics and Computer Science , Georgia State University , Atlanta, GA, 30303;2. Department of Mathematics , College of William and Mary , Williamsburg, VA, 23185 |
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| Abstract: | We characterize the n-by-n sign pattern matrices that require all real, all nonreal, and all pure imaginary eigenvalues. Characterization of sign patterns that allow a real eigenvalue and those that allow a nonreal eigenvalue then follow. Some related specialized results and a characterization of sign patterns that allow a positive real eigenvalue are included. |
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