[math-fun] Hopefully simple question re matrices

Euclidean algorithm / continued fraction on *square matrices* ?? 3 issues: left/right variants; how to stop; how to get "smaller" remainder. Left/right variants: I accept that non-commutativity will produce 2 variants. How to stop: det(remainder)=0 What is the definition of "smaller" in: remainder = dividend - quotient*divisor, such that norm(remainder)<norm(divisor) I.e., what should be the definition of norm(), or are there multiple definitions that work?