Isotropy groups of the action of orthogonal congruence on Hermitian matrices

We present a procedure which enables the computation and the description of structures of isotropy subgroups of the group of complex orthogonal matrices with respect to the action of *congruence on Hermitian matrices. A key ingredient in our proof is an algorithm giving solutions of a certain rectangular block (complex -alternating) upper triangular Toeplitz matrix equation. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY -NC license (http:// creativecommons .org /licenses /by -nc /4 .0/).