SingularValueDecomposition

SingularValueDecomposition[m] gives the singular value decomposition for a numerical matrix m as a list {u, σ, v}, where m = u.σ.ConjugateTranspose[v].

Examples

SVD of a matrix:

{u, s, v} = SingularValueDecomposition[{{1, 2}, {3, 4}}]
(* {{{-0.404, -0.915}, {-0.915, 0.404}}, {{5.46, 0}, {0, 0.366}}, ...} *)

Reconstruct the original matrix:

u . s . ConjugateTranspose[v]
(* {{1., 2.}, {3., 4.}} *)

Please visit the official Wolfram Language Reference for more details.