Which operation is getting applied to the model first when we apply a product of matrices? Consider rotating a point
. We have two rotation matrices and . If we rotate using , we obtain . If we then apply , we get . Now suppose that we instead want to first combine the two rotations and then apply them to to get . Programmers are often temped to combine them as because we read from left to right and also write sequences in this way. However, it is backwards for linear algebra because is already acting from the left side. Thus, it ``reads'' from right to left.^{3.1} We therefore must combine the rotations as to obtain . Later in this chapter, we will be chaining together several matrix transforms. Read them from right to left to understand what they are doing!

Steven M LaValle 2020-01-06