Home/Algebra/Vector spaces/Linear independence18. Vector spacesLinear independenceLevel: intermedioIn 18. Vector spacesFormulaCopy LaTeX∑icivi=0⇒c1=⋯=ck=0\sum_i c_iv_i=0\Rightarrow c_1=\cdots=c_k=0i∑civi=0⇒c1=⋯=ck=0Tagsalgebraspaces vectoralgebra formulalinearDetailNo vector in the set is redundant.Explore the ideaFound an error? Contact us.Related formulasRelatedSpanspan(v1,…,vk)={∑icivi}\operatorname{span}(v_1,\ldots,v_k)=\{\sum_i c_iv_i\}span(v1,…,vk)={i∑civi}Open formulaOpen in sectionRelatedBasis and dimensiondim(V)=#{vectores on una base}\dim(V)=\#\{\text{vectores on una base}\}dim(V)=#{vectores on una base}Open formulaOpen in section