Check out this example with pies: http://www.mathsisfun.com/algebra/matrix-multiplying.html http://www.mathsisfun.com/algebra/matrix-multiplying.html Now, you

Check out this example with pies: http://www.mathsisfun.com/algebra/matrix-multiplying.html http://www.mathsisfun.com/algebra/matrix-multiplying.html Now, you might often see this particular problem in terms of database queries, and that is fine. But the uses I have seen of linear algebra in machine learning are essential to achieving performance. There, the algorithms are often highly iterative, using the same exact source data. To perform such calculations with a loop is extremely inefficient. Even chasing pointers can be a significant cost. There is a reason why Fortran code is generally faster than C for linear algebra out of the box. Also see: http://stackoverflow.com/a/146186 http://stackoverflow.com/a/146186