svd
Singular value decomposition (SVD) is a factorization of a real or complex matrix that expresses the matrix as a product of three simpler matrices. For A in R^{m×n}, the SVD writes A = U Σ V^T (or A = U Σ V^* in the complex case), where U is an m×m orthogonal (or unitary) matrix, V is an n×n orthogonal (or unitary) matrix, and Σ is an m×n diagonal (more precisely, rectangular diagonal) matrix with nonnegative real numbers on its diagonal.
The diagonal entries of Σ are the singular values, usually arranged in nonincreasing order: σ1 ≥ σ2 ≥ … ≥ σp
Key relationships: the nonzero singular values squared are the eigenvalues of A^T A and of A A^T.
Interpretation and uses: the singular values measure how A stretches space along the corresponding singular vectors.