Home/Algebra/Matrix decompositions/QR decomposition23. Matrix decompositionsQR decompositionLevel: avanzadoIn 23. Matrix decompositionsFormulaCopy LaTeXA=QRA=QRA=QRTagsalgebradecompositionsdecompositions matricesalgebra formulalinearDetailQ has orthonormal columns and R is upper triangular.Explore the ideaComputational complexityShow (CS mode)Found an error? Contact us.Related formulasRelatedOrthogonal matrixQTQ=I⇒Q−1=QTQ^TQ=I\Rightarrow Q^{-1}=Q^TQTQ=I⇒Q−1=QTOpen formulaOpen in sectionRelatedGram–Schmidtuk=vk−∑j<kprojuj(vk)u_k=v_k-\sum_{j<k}\operatorname{proj}_{u_j}(v_k)uk=vk−j<k∑projuj(vk)Open formulaOpen in sectionRelatedLeast-squares problemx^=argminx∥Ax−b∥22\hat x=\arg\min_x\|Ax-b\|_2^2x^=argxmin∥Ax−b∥22Open formulaOpen in section