Conjugate reversibility in complex special linear groups

We introduce and study conjugate reversibility (or c-reversibility) in the complex special linear group (n,) where an element is conjugate to the inverse of its complex conjugate. We prove that in (n, ), every c-reversible element is strongly c-reversible. We provide a complete classification of c-reversible elements based on their conjugacy invariants. This leads to an algebraic characterization of projective transformations. As a special case, a finer classification in (4, ) is obtained in terms of trace conditions and resultant computations.