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, . . . , u_n] and 𝗩 = [v₁, . . . , v_n] so that 𝗨^T𝗠𝗩 = Σ with Σ = diag(σ₁, . . . , σ_n). The columns of 𝗨 and 𝗩 are the left and right singular vectors of 𝗠, respectively, the σ_i are the singular values, and 𝗠u_i = σ_iv_i.