Suppose A is an m n matrix of rank r < n. Prove that there exist
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Suppose A is an m × n matrix of rank r < n. Prove that there exist arbitrarily close matrices of maximal rank, that is, for every ε > 0 there exists an m × n matrix B with rank B = n such that the Euclidean matrix norm ΙΙ A − B ΙΙ < ε.
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