Hello. Binary matrices consisting of zero and one may or may not have left inverse in GF(2). How can we impose the condition that a matrix has a left inverse in GF(2) in CVX? Regarding the fact that a square matrix has a determinant of zero or one.

Doesn’t sound (mixed-integer) convex to me. But if you or some algebra guru have a clever formulation, please present it.

Edit: See my later post.

Thanks for your attention.

Is it possible to use LU decomposition or Gaussian elimination inside the CVX block such that gf(2) rules are respected?

Perhaps the program to address the original question could be a feasibility problem (no objective, unless otherwise needed) consisting of the declaration of a bunch of binary variables and a bunch of linear constraints which would be the linearization of `n^2`

bilinear binary equality constraints enforcing `L*M == eye(n)`

, where `L`

is the putative left inverse of the binary matrix `M`

. I leave the details to you.

Thanks for your suggestion. I keep working on it until I get results.