Suppose A is an m ×n matrix of rank r

Question

Suppose A is an m ×n matrix of rank r<n. Prove that there exist arbitrarily close matrices of ma

Accepted Answer

Step 1: Understand the problem statement. We are given a matrix $A$ of size $m u005Ctimes n$ with ra

Suppose $A$ is an $m \times n$ matrix of rank $r<n$. Prove that there exist arbitrarily close matrices of maximal rank, that is, for every $\varepsilon>0$ there exists an $m \times n$ matrix $B$ with rank $B=$ nsuch that the Euclidean matrix norm $\|A-B\|<\varepsilon$.