31. Change of Basis; Image Compression
OK. So, coming nearer the end of the course, this lecture will be a mixture of the linear algebra that comes with a change of basis. And a change of basis from one basis to another basis is something you really do in applications. And, I would like to talk about those applications. I got a little bit involved with compression. Compressing a signal, compressing an image. And that's exactly change-of-basis. And then, the main theme in this chapter is th- the connection between a linear transformation, which doesn't have to have coordinates, and the matrix that tells us that transformation with respect to coordinates. So the matrix is the coordinate-based description of the linear transformation. Let me start out with the nice part, which is just to tell you something about image compression. Those of you -- well, everybody's going to meet compression, because you know that the amount of data that we're getting -- well, these lectures are compressed. So that,...