“…Fix K ∈ {R, C} and denote M n (K) the set of (n × n)-matrices with entries in K. Write the transpose of A ∈ M n (K) by A T and the conjugate transpose by A H . If we fix a non-singular symmetric or Hermitian M ∈ M n (K), then we get the following Lie and where P = T when K = R or P = H when K = C. This provides us with a general framework to study important classes of structured matrices like the ones of Hamiltonian, skew-Hamiltonian, symmetric, skew-symmetric, pseudosymmetric, persymmetric, Hermitian, skew-Hermitian, pseudo-Hermitian, pseudo-skew-Hermitian matrices and so on (see [5,6]). …”