Editing Singular value decomposition (section)

===Compact SVD===

The compact SVD of a matrix {{tmath|\mathbf M}} is given by

<math display=block>
\mathbf{M} = \mathbf U_r \mathbf \Sigma_r \mathbf V_r^*.
</math>

Only the {{tmath|r}} column vectors of {{tmath|\mathbf U}} and {{tmath|r}} row vectors of {{tmath|\mathbf V^*}} corresponding to the non-zero singular values {{tmath|\mathbf \Sigma_r}} are calculated. The remaining vectors of {{tmath|\mathbf U}} and {{tmath|\mathbf V^*}} are not calculated. This is quicker and more economical than the thin SVD if {{tmath|r \ll \min(m,n).}} The matrix {{tmath|\mathbf U_r}} is thus {{tmath|m \times r,}} {{tmath|\mathbf \Sigma_r}} is {{tmath|r \times r}} diagonal, and {{tmath|\mathbf V_r^*}} is {{tmath|r \times n.}}