Field Formation of Circulant Matrix

Abstract

The axioms of fields satisfy over sets of numbers such as Q, R, and C. Generally, a set of matrix is not commutative for binary multiplication properties, such that cannot satisfy of field axioms. In this paper we will discuss circulant matrix set [CIRCn(a)] which satisfy the commutative properties of multiplication, then it will be shown that the definition of a field is satisfied by circulant matrix [CIRCn*(a)] . This can provide new perspective on a field formed by matrix.