Outer Theta and Theta Outer Inverses

In this paper, a new set of matrices - outer theta matrices and theta outer matrices are defined. These classes of matrices serve as outer inverses of (Formula Presented)where (Formula Presented) is the s-conjugate transpose of s-g inverse of A provided it exists. Certain characterizations of outer theta matrices and theta outer matrices are given here. Also, the integral and limit representations of both outer theta and theta outer matrices are explained. To demonstrate their application, some system of linear equations are solved using these matrices.