• STUDY ON SOME PROPERTIES OF SKEW-SYMMETRIC AND SKEW-CIRCULANT MATRIX OVER SKEW FIELD

Abstract

In this paper, some properties of skew-symmetric and skew-circulant matrix were extended from general complex domain to skew field. The relationships between skew-symmetric and skew-circulant matrix and symmetric circulant matrix, symmetric and skew-circulant matrix and skew-circulant matrix, over skew field, were obtained.       Meanwhile, the linear expression of skew-symmetric and skew-circulant matrix under fundamental skew-circulant matrix was also obtained. In addition, over skew field, the sufficient condition, which could infer that one matrix was skew-symmetric and skew-circulant matrix and that skew-symmetric and skew-circulant matrices were            commutative, as well as some properties of inverse matrix of skew-symmetric and skew-circulant matrix were acquired