Rant: Matrices Are Not Arrays of Numbers

The following is an excerpt from a current work of mine. I thought I'd share it here, as some people have told me they enjoyed it. As I'll stress repeatedly, a matrix represents a linear map between two vector spaces. Writing it in the form of an matrix is merely a very convenient way to see the map concretely. But it obfuscates the fact that this map is, well, a map, not an array of numbers.