Finding Near Rank Deficiency in Matrix Products
This paper gives a theorem characterizing approximately minimal norm rank one perturbations E and F that make the product (A + E)(B + F)T rank deficient. The theorem is stated in terms of the smallest singular value of a particular matrix chosen from a parameterized family of matrices by solving a nonlinear equation. Consequently, it is analogous to the special case of the Eckhart-Young theorem describing the minimal perturbation that induces an order one rank deficiency. While the theorem...[Show more]
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