Home/Algebra/Orthogonality and projections/Gram–Schmidt21. Orthogonality and projectionsGram–SchmidtLevel: avanzadoIn 21. Orthogonality and projectionsFormulaCopy LaTeXuk=vk−∑j<kprojuj(vk)u_k=v_k-\sum_{j<k}\operatorname{proj}_{u_j}(v_k)uk=vk−j<k∑projuj(vk)Tagsalgebraalgebra formulalinearorthogonalityorthogonality projectionsDetailBuilds an orthogonal or orthonormal basis from independent vectors.Explore the ideaFound an error? Contact us.Related formulasRelatedOrthogonal projectionprojb(a)=a⋅b∥b∥2b\operatorname{proj}_b(a)=\frac{a\cdot b}{\|b\|^2}bprojb(a)=∥b∥2a⋅bbOpen formulaOpen in sectionRelatedQR decompositionA=QRA=QRA=QROpen formulaOpen in section