Some Research On Special Matrices Over Skew Field

In this paper we discuss the properties of idempotent matrices, EP matrices, GP matrices,HGP matrices,block matrices and nilpotent matrices over skew field. We characterize the nonsingularity of left linear combinations of idempotent matrices over skew field; describe the properties of EP matrices under,GP matrices and HGP matrices of the quaternion field under partially ordering; answer the question of [20] - the exist and the presentation of the groop inverse of the block matrices over skew field,and get the presentation of the groop inverse of EPmatrix; show that nilpotent matrices of skew field could be centralized,give its Jordan criterion form .