eigendecomposition

Eigendecomposition is the factoring of a square matrix into its eigenvalues and eigenvectors—the fundamental components that reveal the matrix's behavior under transformation.

A matrix that can be eigendecomposed is expressed as the product of three matrices: one containing eigenvectors, one containing eigenvalues along its diagonal, and the inverse of the first.

The technique is central to linear algebra and appears throughout physics, statistics, and machine learning: Principal component analysis relies on eigendecomposition of the covariance matrix.