I'm an applied mathematician and this is the most common layout for dense matrices due to BLAS and LAPACK. Note, many of these routines have a flag to denote when working with a transpose, which can be used to cheat a different memory layout in a pinch. There are also parameters for increments in memory, which can help when computing across a row as opposed to down a column, which can also be co-opted. Unless there's a reason not to, I personally default to column major ordering for all matrices and tensors and use explicit indexing functions, which tends to avoid headaches since my codes are consistent with most others.
Abstractly, there's no such thing as memory layout, so it doesn't matter for things like proofs, normally.
Abstractly, there's no such thing as memory layout, so it doesn't matter for things like proofs, normally.