Oops! The "A x B = C" figure is exactly backwards. A matrix with shape (r, k) times a matrix with shape (k, c) should return a matrix with shape (r,c). The figure incorrectly claims that a matrix (k,m) times a matrix with shape (n,k) returns a matrix with shape (n,m), which is only true if all of these numbers are equal (eg. square matrices).

Kind of an embarrassing typo for an article that is essentially about matrix multiplication.

Here is a corrected (transposed) version of that figure: http://i.imgur.com/Bo6CJCv.png

Edit: It looks like every figure in the article suffers from this problem. I know FORTRAN matrices store each column contiguously in memory, but whether a matrix is accessed like * (ptr + r * ncols + c) or * (ptr + c * nrows + r) is (in my opinion) a low-level detail and shouldn't affect our thinking about how multiplication works.