Relationships between fixed points and eigenvectors in the group GL (2, ℝ)

Abstract

PSL(2, R) is the most frequently studied subgroup of the Mobius transformations. By adding anti-automorphisms

G' = {a'z + b'/c'z + d' : a', b', c', d' is an element of R, a'd' - b'c' = -1}

to the group PSL(2, R), the group G = PSL(2, R) boolean OR G' is obtained. The elements of this group correspond to matrices of GL(2, R). In this study, we consider the relationships between fixed points of the elements of the group G and eigenvectors of matrices corresponding to the elements of this group.