Generating $n\times n$ random matrix with rank $n/2$ using matlab

Question

Can we generate $n \times n$ random matrix having any desired rank? I have to generate a $n\times n$ random matrix having rank $n/2$.

Thanks for your time and help.

score 6 · Accepted Answer · answered Apr 16 '13 at 05:33

6

Generate $U,V$ random matrices of size $n \times n/2$, then almost surely $A = U \cdot V^T$ is of rank $n/2$.

answered Apr 16 '13 at 05:33

3

(+1) Unless, of course, $n$ is odd. ;-) – Cameron Buie Apr 16 '13 at 05:39
@user17762 Thank you very much. It works. Can we say anything about what distribution will it follow? – Srijan Apr 16 '13 at 05:56

1 Answers1