Singular value decomposition

From Glossary of Meteorology

singular value decomposition

A numerical procedure to bring a matrix on diagonal form with its singular values on the diagonal.

For a given matrix 𝗠 the method finds orthogonal matrices 𝗨 = [u1, . . . , un] and 𝗩 = [v1, . . . , vn] so that 𝗨T𝗠𝗩 = Σ with Σ = diag1, . . . , σn). The columns of 𝗨 and 𝗩 are the left and right singular vectors of 𝗠, respectively, the σi are the singular values, and 𝗠ui = σivi.