I am trying to parse this paper. The authors at one point make use of a property that a matrix being not regular is equivalent to its null space being not empty. They don't have a reference for this claim and i was just wondering if this is something that's well known? I looked up stuff about regular matrices and the few things i looked at point to the matrix or any of its power being positive element wise. I am not quite sure how that ties to how the authors in this paper used it.
I am attaching a screenshot of the section where they used this property. Any help will be appreciated. Cheers!
