Singular value decomposition (SVD)

Layer 0 — Mathematicsin the linear-algebra subtree

Any m×n matrix A factors as A = UΣV*, with U, V unitary and Σ diagonal with non-negative entries (singular values). Generalizes eigendecomposition to rectangular and non-normal matrices.

Related concepts

Spectral theorem
Matrix and determinant
Tensor decomposition
Principal Component Analysis
Vector space
Polar decomposition
Moore-Penrose pseudoinverse
Accretion disk
PCA via SVD: centred X = UΣVᵀ, Eckart-Young best rank-k in Frobenius
SVD σ₁ of [[3],[4]] = 5 (Pythagorean-Frobenius witness)

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