Exploring the Affine Geometry of Outer Inverses through Computational Experiments

In the paper [19], it is shown that inner inverses exhibit a linear behavior. However, for outer inverses, the types of varieties that can arise are not yet well understood. In fact, the examples presented in [19] illustrate two different situations: in the first, the resulting set is an affine linear variety, while in the second, it can be decomposed as a union of affine algebraic varieties that are not necessarily linear. In this work, we explore several additional examples, which have been generated symbolically using Maple. We observe that for row or column matrices, the resulting sets once again form linear varieties whose dimension equals the number of rows or columns, minus 1, respectively. Thus confirming the behavior observed in [19].