Home/Algebra/Linear transformations/Linearity19. Linear transformationsLinearityLevel: intermedioIn 19. Linear transformationsFormulaCopy LaTeXT(au+bv)=aT(u)+bT(v)T(au+bv)=aT(u)+bT(v)T(au+bv)=aT(u)+bT(v)Tagsalgebraalgebra formulalineartransformationstransformations linearDetailA linear transformation preserves linear combinations.Explore the ideaFound an error? Contact us.Related formulasRelatedLinear combinationw=c1v1+⋯+ckvkw=c_1v_1+\cdots+c_kv_kw=c1v1+⋯+ckvkOpen formulaOpen in sectionRelatedMatrix transformationT(x)=AxT(x)=AxT(x)=AxOpen formulaOpen in section