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Jul 9, 2015 at 19:14 comment added Christopher Drupieski I have updated my answer to reflect the "positive" assumption.
Jul 9, 2015 at 17:03 history edited Christopher Drupieski CC BY-SA 3.0
Corrected my explanation to more accurately match the OP's question.
Jul 9, 2015 at 15:41 comment added Jim Humphreys The assumption was that $m,n$ are both "positive" (which often means strictly positive), so your type of example may not suffice here.
Jul 9, 2015 at 14:12 history answered Christopher Drupieski CC BY-SA 3.0