Understanding Eigenvectors, Eigenvalues, and Eigenspaces

In this video we discuss eigenvectors, eigenvalues, and eigenspaces. Eigen this, eigen that, eigen everywhere! But what does it all mean? I first show how you find eigenvalues, which can then be used to find an eigenspace. The eigenspace yields a basis of eigenvectors! We show visually how it all works with an example and how eigen really just means to "resist a transform" and just scale instead! Example was pulled from Howard Antons "Elementary Linear Algebra" Ed. 10