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I want to find matrices $X$ such that the diagonal of $X^H X$, where $X^H$ is the Hermitian transpose of $X$, is sparse — as many zeros as possible. Intuitively, $X$ should have many empty columns.

I guess this is one of the sparse matrix recovery problems, but I have trouble describing this constraint in a way that could make it amenable to existing algorithms. Can someone please give me pointers to papers/software?

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  • $\begingroup$ nuclear norm or trace norm $\endgroup$ Feb 27, 2018 at 16:22
  • $\begingroup$ Welcome to MSE. I suggest that you add reference-request to your tags. $\endgroup$ Feb 27, 2018 at 16:22
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    $\begingroup$ Why not use the zero matrix? $\endgroup$ Feb 28, 2018 at 7:31
  • $\begingroup$ @RodrigodeAzevedo there are other constraints of course. I was hoping to encourage solutions that have empty row/columns, not just sparse. $X^HX$ being sparse does not fully convey my requirement here. $\endgroup$ Feb 28, 2018 at 19:38
  • $\begingroup$ So, what constraints do you have? $\endgroup$ Mar 2, 2018 at 19:01

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