Centrosymmetric property of unitary matrices that preserve the set of (T plus H)-matrices under similarity transformations

摘要

The following problem is discussed: what are unitary n x n matrices U that map the linear space of (T + H)-matrices into itself by similarity transformations? Analogous problems for the spaces of Toeplitz and Hankel matrices were solved recently. For (T + H)-matrices, the problem of describing appropriate matrices U appears to be considerably more complex and is still open. The result proved in this paper may contribute to the complete solution of this problem. Namely, every such matrix U is either centrosymmetric or skew-centrosymmetric; moreover, only the first variant is possible for odd n.