What Exactly are Eigenvalues and Eigenvectors? What is the point of them? Why do we learn about it?

Many videos and textbooks just tell you how you how to determine eigenvalues and eigenvectors. However, there is often very little contextualization. What are they? What is the point of doing it? What is the value and purpose of determining them? This video answers all these questions. 00:00 – What are eigenvalues and eigenvectors? What is the point of doing it? 06:50 – Significance of eigenvectors - what it means in real life 09:30 – Derivation of characteristic equation 12:00 – Simple example