Spectral study of {R,s+1,k}- and {R

Classification of linear operators satisfying $(Au,v)=(u,A^rv)$ or $(Au,A^rv)=(u,v)$ on a vector space with indefinite scalar product

“…λ R is determined in (5), and Each system ( 15) is reduced by transformations ( 16) with R = F 1 and S = I n to a system of the form…”

“…This research was inspired by the articles [3,4,5,12,13,14,15,16], in which Catral, Lebtahi, Romero, Stuart, Thome, and Weaver study {R, s + 1, k}-potent (respectively, {R, s+1, k, * }-potent) matrices; i.e., those matrices A ∈ C n×n that satisfy RA = A s+1 R (respectively, RA * = A s+1 R), in which R ∈ C n×n is a given matrix satisfying R k = 1 and s, k are positive integers; compare with (1) and (3).…”