I am trying to generate (randomly) set of square matrices $\{K_m\}$ with the properties that $$\sum_{i=1}K_i^{\dagger}.K_i=I_n,$$ where $I_n$ is the identity matrix of order $n$. So, the input should be $m$ and $n$, and in each run the code should generate one set of $K_m$.

I could generate them using a random probability vector and random unitary matrices, but I guess there are other ways.

  • $\begingroup$ That's a conjugate transpose in your sum, yes? $\endgroup$ – J. M. will be back soon Apr 22 '16 at 1:17
  • $\begingroup$ Yes...sorry for not mentioning. $\endgroup$ – Marcus Apr 22 '16 at 1:37

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