Home/Algebra/Orthogonality and projections/Orthogonal projection21. Orthogonality and projectionsOrthogonal projectionLevel: intermedioIn 21. Orthogonality and projectionsFormulaCopy LaTeXprojb(a)=a⋅b∥b∥2b\operatorname{proj}_b(a)=\frac{a\cdot b}{\|b\|^2}bprojb(a)=∥b∥2a⋅bbTagsalgebraalgebra formulalinearorthogonalityorthogonality projectionsDetailProjects a vector onto the direction of another.Explore the ideaFound an error? Contact us.Related formulasRelatedDot productu⋅v=∑iuivi=∥u∥∥v∥cosθ\mathbf u\cdot\mathbf v=\sum_i u_iv_i=\|u\|\|v\|\cos\thetau⋅v=i∑uivi=∥u∥∥v∥cosθOpen 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