Eigenvalues and Eigenvectors
Directions That Only Scale
Discover the special directions a matrix never rotates — only stretches or shrinks. Eigenvalues and eigenvectors reveal the hidden structure of a linear transformation and unlock powerful tools in data science, physics, and differential equations.
Sections
What Is an Eigenvector?
12 min · 3 quiz questions · Interactive diagram
The Eigenvalue Equation
12 min · 3 quiz questions
The Characteristic Polynomial
15 min · 3 quiz questions · Interactive diagram
Computing Eigenvectors
15 min · 3 quiz questions
Eigenspaces and Multiplicity
12 min · 3 quiz questions
Diagonalization
18 min · 3 quiz questions · Interactive diagram
Why Eigenvalues Matter
10 min · 3 quiz questions
The Least Squares Problem
12 min · 3 quiz questions
The Normal Equations
12 min · 3 quiz questions
QR Factorization for Least Squares
12 min · 3 quiz questions · Interactive diagram
Fitting Lines, Parabolas, and Planes
10 min · 3 quiz questions