Characterizations of \(\{K,s+1\}\)-potent matrices and applications
The authors introduce a new kind of matrices called \(\{ K, s+1\}\)-potent as an extension of generalized inverse matrices and involutory matrix, which is the generalization of the well-known idempotent matrix. Then they show that for each positive integer \(n\) there exists at least one \(n \times n\) size matrix that belongs to this class and they also present a method to construct an infinite number of \(\{K, s+1\}\)-potent matrices from only one of them. Moreover, they study sums, products, direct sums and inverse of \(\{K, s+1\}\)-potent matrices. Furthermore, the authors present the characterization of \(\{K, s+1\}\)-potent matrices from a spectral point of view, in terms of powers of the matrix, by means of the group inverse, and via block representation of a matrix of index 1. Then they give conditions under which a linear combination of two commuting \(\{K, s+1\}\)-potent matrices is \(\{K, s+1\}\)-potent.
scientific article; zbMATH DE number 5987840
scientific article