Some norm inequalities concerning generalized inverses
Philip J. Maher · Linear Algebra and its Applications · 1992
We extend to the von Neumann-Schatten classes Cp and norms | · |psome inequalities concerning generalized inverses. We extend Penrose's result on minimizing | AX − B|2 to the | · |p norm. We also minimize | X |p where X varies such that (1) B = A−AX = A−AB and (2) A∗AX = A∗ (in both cases A, B fixed). Local considerations are adduced: in each result here global minima and critical points coincide.