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 $m \times n$?
It is generally a good idea to keep things alphabetical, unless there is a good reason to do otherwise.


With matrices, it can be okay because an $n\times m$ matrix is really a linear transformation from $\mathbb{F}^m\to \mathbb{F}^n$ (where $\mathbb{F}$ is your field of definition), and so viewed this way, the $m$-dimensional space comes before the $n$-dimensional space.


So I think you are okay sticking with what you have.


