The Congruent Centralizer of the Horn–Sergeichuk Matrix

Abstract

The paper describes the congruent centralizer of the matrix \( {\Delta}_n=\left(\begin{array}{llll}\hfill & \hfill & \hfill & 1\hfill \\ {}\hfill & \hfill & \dots \hfill & i\hfill \\ {}\hfill & 1\hfill & \dots \hfill & \hfill \\ {}1\hfill & i\hfill & \hfill & \hfill \end{array}\right) \), representing one of three blocks in the Horn–Sergeichuk canonical form, i.e., the set of matrices X such that X^∗Δ_nX = Δ_n.