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The numerical range of a nonnegative matrix |
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| Authors: | Chi-Kwong Li Bit-Shun Tam and Pei Yuan Wu |
| Institution: | a Department of Mathematics, College of William and Mary, Williamsburg, VA 23187, USA b Department of Mathematics, Tamkang University, Tamsui, 25137 Taiwan, ROC c Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 30050 Taiwan, ROC |
| Abstract: | We offer an almost self-contained development of Perron–Frobenius type results for the numerical range of an (irreducible) nonnegative matrix, rederiving and completing the previous work of Issos, Nylen and Tam, and Tam and Yang on this topic. We solve the open problem of characterizing nonnegative matrices whose numerical ranges are regular convex polygons with center at the origin. Some related results are obtained and some open problems are also posed. |
| Keywords: | Numerical range Nonnegative matrix Irreducible real part Numerical radius Perron–Frobenius theory Regular polygon Sharp point |
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