Some norm inequalities concerning generalized inverses,2.

Maher, Philip (2007) Some norm inequalities concerning generalized inverses,2. Linear Algebra and its Applications, 420 (2-3) . pp. 517-525. ISSN 0024-3795 [Article] (doi:10.1016/j.laa.2006.08.024)

Abstract

We extend to the von Neumann–Schatten classes Cp and norms short parallel·short parallelp, where 2 less-than-or-equals, slant p < ∞, Penrose’s result on minimizing short parallelAXB − Cshort parallel2. We give an example to show that this extension does not hold for 1 less-than-or-equals, slant p < 2. The proof of the global inequality depends on local considerations.

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