I have some data that I share between Python and Matlab. I used to do it by saving NumPy arrays in MATLAB-style .mat files but would like to switch to HDF5 datasets. However
See the Matlab HDF5 documentation which includes the statement:
Because HDF5 stores data in row-major order and the MATLAB array is organized in column-major order, you should reverse the ordering of the dimension extents ...
Even today, long after the Mathworks translated their code to C (etc), the product's Fortran origins poke above the surface now and then.