Singular value decomposition
Also: SVD, singular values, singular vectors
Every m×n matrix can be written A = UΣVᵀ with orthogonal U and V and non-negative singular values on the diagonal of Σ. It underlies PCA, low-rank compression and latent semantic analysis.
A = U Σ Vᵀ
Example
PCA on a centered data matrix X̃ is usually done as SVD: the right singular vectors (columns of V) are the principal components, and σᵢ² / (n − 1) is the variance along each.