DRAZIN’S PSEUDO-INVERSE OF RIGHT ANGLE SINGULAR MATRIX

Abstract

Throughout theoretical investigation that is done in this paper for Drazin’s pseudo inverse in associative ring we have build such an inverse in specific ring. Upper right angle matrices are singular matrices, their determinant is zero which means they don’t have inverse matrices. Properties of Drazin’s pseudo inverse enable us to find so called pseudo inverse of those matrices. In this paper we have construct Drazin’s pseudo inverse for singular matrices in real square matrix ring. We will build the construction according to definition of pseudo-inverse given by Drazin. In case when elements of any ring \(R\) are non-singular then the pseudo-inverse of Drazin becomes inverse that satisfies the condition \(\forall a \in R, \exists a^{-1} \in R, a \cdot a^{-1} = e\), where \(e\) is identity element in \(R\).