Home/Algebra/Matrix decompositions/SVD23. Matrix decompositionsSVDLevel: avanzadoIn 23. Matrix decompositionsFormulaCopy LaTeXA=UΣVTA=U\Sigma V^TA=UΣVTTagsalgebradecompositionsdecompositions matricesalgebra formulalinearreductionDetailUniversal decomposition into singular directions and scales.Explore the ideaComputational complexityShow (CS mode)Found an error? Contact us.Related formulasRelatedPseudoinversex^=A+b;A+=VΣ+UT\hat x=A^+b;\quad A^+=V\Sigma^+U^Tx^=A+b;A+=VΣ+UTOpen formulaOpen in sectionRelatedLow-rank approximationAk=∑i=1kσiuiviTA_k=\sum_{i=1}^{k}\sigma_i u_i v_i^TAk=i=1∑kσiuiviTOpen formulaOpen in sectionRelatedFrobenius norm∥A∥F=∑i=1m∑j=1n∣aij∣2.\|A\|_F = \sqrt{\sum_{i=1}^{m}\sum_{j=1}^{n}|a_{ij}|^2}.∥A∥F=i=1∑mj=1∑n∣aij∣2.Open formulaOpen in sectionRelatedSpectral norm∥A∥2=σmax(A).\|A\|_2 = \sigma_{\max}(A).∥A∥2=σmax(A).Open formulaOpen in sectionRelatedCondition numberκ(A)=∥A∥ ∥A−1∥.\kappa(A) = \|A\|\,\|A^{-1}\|.κ(A)=∥A∥∥A−1∥.Open formulaOpen in section