On Unitary and Symmetric Matrices With Real Quaternion Elements

Abstract

1. Introduction. In general when symmetric matrices are considered, the elements of the matrix are taken at least in a principal ideal ring. It is interesting to determine what can be attained when the elements are not, in general, commutative and, to this end, the following is concerned with symmetric matrices with elements in the non-commutative field of real quaternions. At the same time some properties of real quaternion unitary matrices are obtained which involve symmetric matrices.