I believe no… but math has a way of surprising me… I don’t know half of it… E.g. I didn’t give this much though until I realized (with more advanced “numbers” they lose more properties):
For complex number (and matrices of anything, except trivial 1x1?) < is not defined. Other than that, I believe when < is defined, it’s always defined the same way. Otherwise, I’m in trouble… and I really need to know.