0000000001155937
AUTHOR
Jeffrey Stuart
On a matrix group constructed from an {R,s+1,k}-potent matrix
Let R is an element of C-nxn be a {k}-involutory matrix (that is, R-k = I-n) for some integer k >= 2, and let s be a nonnegative integer. A matrix A is an element of C-nxn is called an {R,s + 1, k}-potent matrix if A satisfies RA = A(s+1)R. In this paper, a matrix group corresponding to a fixed {R,s + 1, k}-potent matrix is explicitly constructed, and properties of this group are derived and investigated. This group is then reconciled with the classical matrix group G(A) that is associated with a generalized group invertible matrix A.
Matrices A such that R A = A^{s + 1} R when R^k = I
This paper examines matrices A∈C^(n×n) such that R A = A^(s+1) R where R^k = I, the identity matrix, and where s and k are nonnegative integers with k⩾2. Spectral theory is used to characterize these matrices. The cases s = 0 and s⩾1 are considered separately since they are analyzed by different techniques.