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Abstract
Some well-known characterizations of nonnegative k-potent matrices have been obtained by Flor [P. Flor, On groups of nonnegative matrices, Compositio Math. 21 (1969), pp. 376–382.] and Jeter and Pye [M. Jeter and W. Pye, Nonnegative (s, t)-potent matrices, Linear Algebra Appl. 45 (1982), pp. 109–121.]. In this article, we obtain a structural characterization of a real k-potent matrix A, provided that (sgn(A)) k+1 is unambiguously defined, regardless of whether A is nonnegative or not.
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Acknowledgements
The authors thank the referee for many valuable and detailed suggestions. Work by R. Huang was supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20094301120002), China Postdoctoral Science Foundation (No. 20090451103) and the Research Found of Education Bureau of Hunan Province (No. 09C942). Work by J. Liu was supported by NSFC Grant 10971176. Work by L. Zhu was supported by the Natural Science Found of Hunan Province (No. 08JJ6038).