Lecture 4: Eigenvalues and Eigenvectors

Description

Professor Strang begins this lecture talking about eigenvectors and eigenvalues and why they are useful. Then he moves to a discussion of symmetric matrices, in particular, positive definite matrices.

Summary

\(Ax =\) eigenvalue times \(x\)
\(A^2x =\) (eigenvalue)\(^2\) times \(x\)
Write other vectors as combinations of eigenvectors
Similar matrix \(B = M^{-1}AM\) has the same eigenvalues as \(A\)

Related section in textbook: I.6

Instructor: Prof. Gilbert Strang