Symmetric matrix as a linear transformation operators in vector space has the real eigenvalues and corresponding real orthogonal eigenvectors. Gonerally, these properties are premised in IE approach on quantative analysis of management system because which brings simpleness in computation and anaysis. However, when considered symmetric matrix is a special type of matrix forms, we know that its associated properties are partial thing, that is, it consider only maximum moduli eigenvalue for meaningful outputs. On this view point, this study extends symmetric matrix operators to general matrix forms which have real or complex eigensolutions. And we analyze every these eigensolutions in that convergency property for matrix norm and cyclicity for complex eigenvalue of a considered matrix operators.