The moore-penrose inverse of a matrix over a semi-simpie artinian ring
Dirk Huylebrouck, Roland Puystjens, Jan Van Geel · Linear and Multilinear Algebra · 1984
Given an m-by-n matrix over a semi-simple artinian ring with aninvolutory automorphism, necessary and sufficient conditions are given for the matrix tao have a Moore—Penrose inverse. Moreover, expressions for the MP-inverse are obtained. These formulas may be considered as a generalization of the MacDuffee formula for the MP-inverse of a matrix over the complex numbers.