J. Caltenco, J. López-Bonilla, B. Carvajal-Gámez, P. Lam-Estrada
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We study the SVD of an arbitrary matrix , 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.