@meowmeowmeow
5. A diagonal matrix is what it sounds like - all of the (nonzero) entries are on the diagonal, from the top left corner to the bottom right. Why do we care? All sorts of calculations are easier with diagonal matrices, which is great for lazy mathematicians and efficient programmers. Some matrices aren't diagonal, but "diagonalizable," meaning we can shuffle them around into a similar diagonal matrix by using their eigenvectors, which comes in quite handy.