English: Visualize a non-reflexive generalized inverse X of a matrix A, both viewed as linear maps between the vector spaces U and V. X maps A's image to a complemented subspace of its kernel bijectively, and maps a complemented subspace of A's image to part of A's kernel.

Compared with the reflexive case, this case neither guarantees that X's image and A's kernel are disjoint in U, nor that A's image and X's kernel exhaust V.

Here, “K^∁ is a complemented subspace of K” means that their direct sum spans the whole space, yet they intersect only at the zero vector.