Linear Algebra
Advanced

Eigenvalue Equation

Defines eigenvalues and eigenvectors of a matrix.

Formula

Av⃗=λv⃗A\vec{v} = \lambda\vec{v}

Variables

AMatrix
\vec{v}Eigenvector
\lambdaEigenvalue

Example

For A = [[2,0],[0,3]], v = (1,0) is an eigenvector with eigenvalue λ = 2.

Did You Know?

Eigenvectors are the special directions a matrix merely stretches — the math behind Google's original PageRank.

matrixeigenvalueeigenvector