Conversation

Math equations as you typically find them in texts are a lot like optimised code. Like optimised code, they evaluate faster. Like optimised code, they're less intuitive and pedagogical than a naive implementation.

For example, the matrix for rotating a vector around the origin makes a lot more sense if you write it out as a set of three equations - one per axis - because you can actually work out how the sines and cosines act on each other and the point as the rotation angle changes that way.