Comment by owlbite

Oh yes, from an actual implementation POV you can just apply some transpose and ordering transforms to convert from row major to column major or vice-versa. cblas is pretty universal though I don't think any LAPACK C API ever gained as wide support for non column-major usage (and actually has some routines where you can't just pull transpose tricks for the transformation).

Certain layouts have performance advantages for certain operations on certain microarchitectures due to data access patterns (especially for level 2 BLAS), but that's largely irrelevant to historical discussion of the API's evolution.