Power Method for Dominant Eigenvalues and Eigenvectors in Linear Algebra

Explore the power method for approximating dominant eigenvectors and eigenvalues of symmetric matrices in this 21-minute linear algebra video. Learn about power sequences, dominant eigenvalues, and eigenvectors. Follow along with a step-by-step example demonstrating six iterations of the power method, and discover how to use the Rayleigh quotient for eigenvalue approximation. Delve into maximum entry scaling and Euclidean scaling techniques, gaining geometric intuition along the way. Master this crucial numerical analysis technique for solving eigenvalue problems in linear algebra.

Intro
Definition of Power Sequence and Dominant Eigenvalues/Eigenvectors
Dominant Eigenvalue Example
Power Method Approximation
If the Dominant Eigenvalue is Negative
Rayleigh Quotient
Using the Power Method
Start
Arriving at Approximation
Issue of Scale
Maximum Entry Scaling
Euclidean Scaling
Geometric Intuition
Conclusion