Home/Algebra/Least squares/Normal equations22. Least squaresNormal equationsLevel: avanzadoIn 22. Least squaresFormulaCopy LaTeXATAx^=ATbA^TA\hat x=A^TbATAx^=ATbTagsalgebraalgebra formulalinearleast squaresDetailCharacterize the projection of b onto the column space of A.Explore the ideaComputational complexityShow (CS mode)Found an error? Contact us.Related formulasRelatedLeast-squares problemx^=argminx∥Ax−b∥22\hat x=\arg\min_x\|Ax-b\|_2^2x^=argxmin∥Ax−b∥22Open formulaOpen in sectionRelatedPseudoinversex^=A+b;A+=VΣ+UT\hat x=A^+b;\quad A^+=V\Sigma^+U^Tx^=A+b;A+=VΣ+UTOpen formulaOpen in section