On the least squares distance between affine subspaces (Q1914233)

Suppose that two affine subspaces \(L_1, L_2\) of \(\mathbb{R}^n\) are given by consistent systems of linear equations \(Ax=a\) and \(By=b\), respectively. In contrast to an earlier paper [\textit{A. M. DuPré} and \textit{S. Kass}, Linear Algebra Appl. 171, 99-107 (1992; Zbl 0781.51003)] no assumptions are made on the rank of \(A\) or \(B\). Loosely speaking the authors establish a formula for the Euclidean distance of \(L_1, L_2\) in terms of the given vectors \(a,b\), the given matrices \(A,B\), generalized inverses of these matrices (not necessarily the Moore-Penrose inverses) and some extra matrix which is subject to a certain condition involving \(A\) and \(B\). Moreover, the set of feet of the perpendicular bisectors of \(L_1\) and \(L_2\) are described in a similar manner.