Analogs of the adjoint matrix for generalized inverses and corresponding Cramer rules
Ivan Kyrchei · Linear and Multilinear Algebra · 2008
In this article, we introduce determinantal representations of the Moore–Penrose inverse and the Drazin inverse which are based on analogs of the classical adjoint matrix. Using the obtained analogs of the adjoint matrix, we get Cramer rules for the least squares solution and for the Drazin inverse solution of singular linear systems. Finally, determinantal expressions for A + A, A A +, and A D A are presented.