TITLE: Practical uses of matrix multiplication
QUESTION [24 upvotes]: Usually, the use of matrix multiplication is initially given with graphics — scalings, translations, rotations, etc. Then, there are more in-depth examples such as counting the number of walks between nodes in a graph using the power of the graph's adjacency matrix.
What are other good examples of using matrix multiplication in various contexts?

REPLY [6 votes]: Hey Alex, a central theme of Machine Learning is about finding structures (preferably linear ones) in the data space; the intrinsic dimentionalities of your observations if you may (see Eigenfaces).
I understand this may not be about matrix multiplication per se; instead, this is about what, many times, happens right before it. It begins with the spectral theorem: A = SΛS' (inverse when A is non-symmetric); it is Literally the basis of so many things (see what I did there?).