DRAZIN THETA AND THETA DRAZIN MATRICES

In this paper, two new classes of matrices-Drazin-theta matrix and theta-Drazin matrix are introduced for a square matrix of index m. Whenever the index is equal to one, we get special case of matrices called Group-theta matrix and theta-Group matrix respectively. Several characterizations of these matrices, the integral representations, representation in limit form and the representation in terms of rank factorization are obtained. Also, the relationship of Drazin-theta and theta-Drazin matrices with other well known generalized inverses are investigated. By applying the concept of Drazin-theta matrix, general solutions of certain types of matrix equations are characterized here.