Essential Math for Data Science: Basis and Change of Basis - KDnuggets

One way to understand eigendecomposition is to consider it as a change of basis. You'll learn in this article what is the basis of a vector space. You'll see that any vector of the space are linear combinations of the basis vectors and that the number you see in vectors depends on the basis you choose. Finally, you'll see how to change the basis using change of basis matrices. It is a nice way to consider matrix factorization as eigendecomposition or Singular Value Decomposition.