Reducible pattern \(k\)-potent ray pattern matrices
An \(n \times n \) ray pattern is the set of all \(n \times n \) complex matrices with a specified zero-nonzero pattern and with the argument specified for each nonzero entry. A ray pattern \(A\) is said to be pattern \(k\)-potent if \(k\) is the smallest positive integer such that \(A^{k+1} = A\) as ray patterns. The author extends some results of \textit{J. Stuart}, \textit{L. Beasley} and \textit{B. Shader} [Linear Algebra Appl. 346, No. 1--3, 261--271 (2002; Zbl 0998.15030)] to the reducible ray patterns and supplies his article with interesting examples.
scientific article; zbMATH DE number 1880065