Matrices – big scary math things?

You knew we could not avoid it forever, right? It is time to talk briefly about matrices and matrix math. Don't worry! It is not nearly as scary as it sounds at first.

A matrix is really nothing more than a grid of numbers. Mathematically, a matrix can have any number of rows and columns, but in XNA we use 4 by 4 matrices, meaning the matrix has four rows of four columns. Each of these columns contains a number. The XNA Matrix class defines these values as floats, and assigns them names of M11 through M44 (the first number being the row, the second being the column; so M23 is the second row, third column). We will also use 1 by 4 matrices, or matrices with one column and four rows. We have already used them, in fact, though you may not immediately recognize them as 1 by 4 matrices because of the way they are declared in our code. More on that in a moment.

We have used the identity matrix before, and it looks like this:

When we multiply two matrices together...