Ye, Suhua; Chen, Yizhi; Luo, Hui On generalized \(m\)-power matrices and transformations. (English) Zbl 1263.15017 Int. J. Math. Comb. 2012, No. 2, 71-75 (2012). A square matrix \(A\) with complex entries is called a generalized \(m\)-power matrix if there are \(m\) distinct complex numbers \(\lambda_1, \lambda_2,\ldots, \lambda_m\) such that \(\prod_{i=1}^m(A+\lambda_iI)=0\). This definition is introduced in the paper and some characterizations of generalized \(m\)-power matrices in terms of the rank of the factors \(A+\lambda_i I\) are given. Particular emphasis is devoted to \(m\)-idempotent and \(m\)-unit-potent matrices and extensions to generalized \(m\)-power transformations are analyzed. Reviewer: João R. Cardoso (Coimbra) MSC: 15A24 Matrix equations and identities 15B99 Special matrices Keywords:generalized \(m\)-power matrix; generalized \(m\)-power transformations; \(m\)-idempotent matrix; \(m\)-unit-potent matrix PDFBibTeX XMLCite \textit{S. Ye} et al., Int. J. Math. Comb. 2012, No. 2, 71--75 (2012; Zbl 1263.15017)