We study the SVD of an arbitrary matrix Anxm, especially its subspaces of activation, which leads in natural manner to pseudoinverse of Moore-Bjenhammar-Penrose. Besides, we analyze the compatibility of linear systems and the uniqueness of the corresponding solution, and our approach gives the Lanczos classification for these systems.
The Bulletin of Society for Mathematical Services and Standards (Volume 11)
J.H. Caltenco et al., "Singular Value Decomposition", The Bulletin of Society for Mathematical Services and Standards, Vol. 11, pp. 13-20, 2014