Home/Algebra/Vector spaces/Rank–nullity theorem18. Vector spacesRank–nullity theoremLevel: intermedioIn 18. Vector spacesFormulaCopy LaTeXn=rank(A)+nullity(A)n=\operatorname{rank}(A)+\operatorname{nullity}(A)n=rank(A)+nullity(A)Tagsalgebraspaces vectoralgebra formulalineardomain restrictionDetailSplits the domain dimension into preserved and lost information.Explore the ideaFound an error? Contact us.Related formulasRelatedRankrank(A)=dim(Col(A))\operatorname{rank}(A)=\dim(\operatorname{Col}(A))rank(A)=dim(Col(A))Open formulaOpen in sectionRelatedNullitynullity(A)=dim(kerA)\operatorname{nullity}(A)=\dim(\ker A)nullity(A)=dim(kerA)Open formulaOpen in section