Unitary automorphisms of the space of Toeplitz-plus-Hankel matrices

Abstract

Our motivation was a paper of 1991 indicating three special unitary matrices that map Hermitian Toeplitz matrices by similarity into real Toeplitz-plus-Hankel matrices. Generalizing this result, we give a complete description of unitary similarity automorphisms of the space of Toeplitz-plus-Hankel matrices.

Keywords

• Toeplitz matrix
• Hankel matrix
• Toeplitz-plus-Hankel matrix
• centrosymmetric matrix
• skewcentrosymmetric matrix
• unitary similarity automorphism
• 15B05