Tangent and Normal Cones for Low-Rank Matrices
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In (D. R. Luke, J. Math. Imaging Vision, 47 (2013), 231–238) the structure of the Mordukhovich normal cone to varieties of low-rank matrices at rank-deficient points has been determined. A simplified proof of that result is presented here. As a corollary we obtain the corresponding Clarke normal cone. The results are put into the context of first-order optimality conditions for low-rank matrix optimization problems.