Singular value decomposition is a very useful way of solving systems of linear equations, examining interrelationships between data, and in image compression. In today's example, we see how SVD can play an important role in control - a subject you will study a year from now. The example is given here. The "published" version of the example is given here, which may be easier to see.
Another example of the use of SVD is image compression. Using a (relatively) small number of singular values you can reconstruct the original image to a high precision. An example of that is given here. Download the zip file and play with it!