The applications of eigenvectors and eigenvalues - That thing you heard in Endgame has other uses

The video tutorial explains the concepts of eigenvectors and eigenvalues, demonstrating their application in matrix transformations, the Fibonacci sequence, and real-world scenarios like population dynamics and physics. It highlights how eigenvectors and eigenvalues can predict long-term behavior in systems and sequences, and explores advanced applications such as Google PageRank and bipartite graphs.

Explain how eigenvalues can be used to analyze the stability of a system.

How do eigenvectors help in predicting the long-term behavior of a population model?

What role do eigenvalues play in the context of Google PageRank?

How can the concept of eigenvalues and eigenvectors be applied to a bipartite graph?