Things that everyone can agree on:
We have this array:
1 2 3
4 5 6
This is stored as 1 2 3 4 5 6 in row major, and 1 4 2 5 3 6 in column major. Makes sense.
I would call this a 2x3 matrix. BUT do column major/row major consider it to be different?
A(1,2) = 2 seems right to me.
A(1,2) = 4 is this ever true?!
I don't think so...
Maybe we only have to switch things up when we're converting between 2 different programming languages (ie. C and fortran).