Home/Algebra/Vector spaces/Coordinates in a basis18. Vector spacesCoordinates in a basisLevel: intermedioIn 18. Vector spacesFormulaCopy LaTeXv=∑icibi⇒[v]B=(c1,…,cn)Tv=\sum_i c_ib_i\Rightarrow[v]_\mathcal B=(c_1,\ldots,c_n)^Tv=i∑cibi⇒[v]B=(c1,…,cn)TTagsalgebraspaces vectoralgebra formulalinearDetailRepresents a vector by coefficients relative to a basis.Explore the ideaFound an error? Contact us.Related formulasRelatedChange of basis[v]C=PC←B[v]B[v]_\mathcal C=P_{\mathcal C\leftarrow\mathcal B}[v]_\mathcal B[v]C=PC←B[v]BOpen formulaOpen in section