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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.

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

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    $\begingroup$ (+1) Unless, of course, $n$ is odd. ;-) $\endgroup$ – Cameron Buie Apr 16 '13 at 5:39
  • $\begingroup$ @user17762 Thank you very much. It works. Can we say anything about what distribution will it follow? $\endgroup$ – srijan Apr 16 '13 at 5:56

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