Unit 14: Eigenvectors and eigenvalues
About this unit
An eigenvector of A is a nonzero vector that A only scales, Av = λv; the scale factor λ is its eigenvalue. Eigenvalues solve det(A − λI) = 0, and a basis of eigenvectors makes A diagonal.
By the end, you can: Recognise eigenvectors as the directions a transformation only scales, and find eigenvalues and eigenvectors of a 2×2 matrix from det(A − λI) = 0.
Modules
5 modulesLearn
- Directions that stay putArticle · Most vectors are turned off their line by a transformation; eigenvectors stay on their own line and are only scaled, by the eigenvalue.Not started
- Finding eigenvaluesArticle · Av = λv means (A − λI)v = 0 for a nonzero v, so det(A − λI) = 0; solve for λ, then for v. An eigenbasis makes the matrix diagonal.Not started
- Hunt for the eigenvectorsExperiment · Drag the probe until it stays on its line, then find the direction stretched by exactly 1.Not started
- Eigenvectors in briefReview · What eigenvectors and eigenvalues are, how to find them, and what kinds of maps have how many.Not started