An Oblique Matrix Pseudoinverse
R. D. Milne · SIAM Journal on Applied Mathematics · 1968
A singular or rectangular matrix does not have an inverse in the usual sense. Nevertheless a matrix having properties which are closely akin to those of an inverse may be defined for such matrices. This matrix, the pseudoinverse or generalized inverse, has hitherto been uniquely defined for any given matrix. In this paper the concept of the pseudoinverse is widened so as to admit, for any given matrix, of a class of pseudoinverses from which that member may be uniquely selected which has the most convenient properties for a particular application. The conventional pseudoinverse is included in the widened definition. Much of the analysis can be applied to bounded linear operators on Hilbert space.8