I\'m studying simple multiplication of two big matrices using the Eigen library. This multiplication appears to be noticeably slower than both Matlab and Python for the same
The reason Matlab is faster is because it uses the Intel MKL. Eigen can use it too (see here), but you of course need to buy it.
That being said, there are a number of reasons Eigen can be slower. To compare python vs matlab vs Eigen, you'd really need to code three equivalent versions of an operations in the respective languages. Also note that Matlab caches results, so you'd really need to start from a fresh Matlab session to be sure its magic isn't fooling you.
Also, Matlab's Mex overhead is not nonexistent. The OP there reports newer versions "fix" the problem, but I'd be surprised if all overhead has been cleared completely.