this is not true because you impose sparsity
(the way you wrote it is a bit unclear, people might think, if they don't read carefully,
that after sparsifying the condition # > 50).
also, if they do understand, they will wonder what is the condition # after sparsifying.
maybe clarify?
i'd maybe add pseudocode in the appendix to clarify exactly what you did.
it is important for people to be able to reproduce our results from reading the paper
(and better from running the code!)
this is not true because you impose sparsity (the way you wrote it is a bit unclear, people might think, if they don't read carefully, that after sparsifying the condition # > 50). also, if they do understand, they will wonder what is the condition # after sparsifying. maybe clarify?
i'd maybe add pseudocode in the appendix to clarify exactly what you did. it is important for people to be able to reproduce our results from reading the paper (and better from running the code!)