Algorithms to handle what you talk about efficiently is one of the primary reason these libraries even exist. OF COURSE they access memory in the right order; t

Algorithms to handle what you talk about efficiently is one of the primary reason these libraries even exist. OF COURSE they access memory in the right order; that is their job. But it is not really about right vs wrong order, but using an algorithm to tile the data efficiently. Google "Anatomy of High Performance Matrix Multiplication" for examples from OpenBLAS. This is where NumPy falls through -- "a.T + a" will be very slow no matter what you do, but it can be done efficiently with tiling.