6533b7dafe1ef96bd126e7cd

RESEARCH PRODUCT

On a matrix group constructed from an {R,s+1,k}-potent matrix

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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.