Here comes the science.  Well, here comes the math, really, in
which Matrix-Chain-Order gets a little bit sharper around the
edges.  When you multiply a long list of matrices together,
there’s a few (usually one, really) ways of doing that that are
significantly faster than the others. That doesn’t mean you’re
going to get the wrong answer, it’s just that, like much of
life, going about it one way can be much, much faster than the
others.  If you are not interested in this sort of thing,
please, come back tomorrow, where I will try hard to be
entertaining. Right now, you’re getting abstract algebra.  If
you don’t remember your matrix multiplication from high-school
algebra, it works like this: if you’ve got two matrices A1 and
A2, you can only multiply them together if the number of columns
in the first one is the same as the number of rows in the second
one – that is, if your A1 is a 2×5 matrix and your A2 is 5×3,
for example. Then, when you multiply them together, the thing
that comes out will have as many