Abstract
We introduce some new algebraic and topological properties of the Minkowski inverse A(circle plus) of an arbitrary matrix A is an element of M-m,M-n (including singular and rectangular) in a Minkowski space mu. Furthermore, we show that the Minkowski inverse A(circle plus) in a Minkowski space and the Moore-Penrose inverse A(+) in a Hilbert space are different in many properties such as the existence, continuity, norm, and SVD. New conditions of the Minkowski inverse are also given. These conditions are related to the existence, continuity, and reverse order law. Finally, a new representation of the Minkowski inverse A(circle plus) is also derived.