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.
Singular value decomposition (SVD)
Related concepts
- Spectral theorem
- Matrix and determinant
- Tensor decomposition
- Principal Component Analysis
- Vector space
- Polar decomposition
- Moore-Penrose pseudoinverse
- Accretion disk
- MERA (Multi-scale Entanglement Renormalization Ansatz): SVD-based scale-invariant tensor network
- Density matrix renormalisation group (DMRG)
- PCA via SVD: centred X = UΣVᵀ, Eckart-Young best rank-k in Frobenius
- SVD σ₁ of [[3],[4]] = 5 (Pythagorean-Frobenius witness)