Dear friends
Let $\bf{C}$ be a $m \times n$ matrix, where its elements are drawn randomly from a continious distribution, and its rank is $\min (m, n)$ with probability one. For decreasing the rank of $\bf{C}$ to $d$, where $d \le \min(n,m) $; how many elements of $\bf{C}$ should be changed (designed).
For example, ${\bf{A}}$ is a 2-by-2 matrix with random generated elements as follows: A=[1, 2; 3, 4] if I wish to decrease its rank to one, it is necessary to change one of the elements of A, as follows: A_new=[1.5 2; 3 4]
Thanks for your time.