Abstract
A Hankel circulant is a matrix obtained by reversing the order of columns (or rows) in a conventional circulant. A Toeplitz-plus-Hankel circulant (briefly, ()-circulant) is the sum of a circulant and a Hankel circulant. Bozzo discovered that the set of ()-circulants is the centralizer of the matrix , where is the cyclic permutation matrix. As a consequence, all the matrices in can be simultaneously brought to a block diagonal form with diagonal blocks of orders one and two by a unitary similarity transformation. We show that the same assertion holds for if unitary similarities are replaced by unitary congruences.
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