Some Properties of the Exchange Operator with respect to Structured Matrices defined by Indefinite Scalar Product Spaces

• Main Authors: Cheng, Hanz Martin C, David, Roden Jason
• Format: text
• Published: Archīum Ateneo 2015
• Subjects: Scalar Product Spaces; Structured Matrices; Exchange Operator; Algebraic Geometry; Discrete Mathematics and Combinatorics; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/7; https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1006&context=mathematics-faculty-pubs
• Institution: Ateneo De Manila University

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.].