Consider the lowly 2×2 matrix

If you're into computer graphics, you have to love matrices, but sometimes matrices are so complicated. They have determinants, eigenvalues, singular value decompositions... . What does all this stuff really mean? What does it mean, for example, to take the square root of a matrix? How about the logarithm of a matrix? I have built up my intuition about matrices by playing extensively with the simplest form, the lowly 2×2 matrix. These almost look too simple to be interesting, but they show off most of the properties of larger matrices. Better yet, you can write out explicit formulas for quantities that are harder to compute for larger matrices. Even so, some of the derivations provided in this article are probably at the limit of most people's appetite for algebra