The properties of the exchange operator on some types of matrices are explored in this paper. In particular, the properties of exc(A,p,q), where A is a given structured matrix of size (p+q)Ã(p+q) and exc : M ÃNÃN â M is the exchange operator are studied. This paper is a generalization of one of the results in [N.J. Higham. J-orthogonal matrices: Properties and generation. SIAM Review, 45:504â519, 2003.].
Cheng, H.M.C., David, R.J. (2015). Some properties of the exchange operator with respect to structured matrices defined by indefinite scalar product spaces. Electronic Journal of Linear Algebra, 30, Article number 21, 304-311.