For whatever reason, I have always defined matrices as being $n \times m$, and that is how I have been defining matrices throughout my dissertation. Recently however, I have noticed that nearly every other source primarily defines matrices as being $m \times n$. Is the later more formal notation? Should I go through my whole dissertation to change the notation? How important is it?
Is it improper to define matrices as being $n \times m$ rather than $m \times n$?
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