Home/Algebra/Linear transformations/Change of basis19. Linear transformationsChange of basisLevel: avanzadoIn 19. Linear transformationsFormulaCopy LaTeX[v]C=PC←B[v]B[v]_\mathcal C=P_{\mathcal C\leftarrow\mathcal B}[v]_\mathcal B[v]C=PC←B[v]BTagsalgebraalgebra formulalineartransformationstransformations linearDetailConverts coordinates between two bases.Explore the ideaFound an error? Contact us.Related formulasRelatedCoordinates in a basisv=∑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)TOpen formulaOpen in sectionRelatedDiagonalizationA=PDP−1A=PDP^{-1}A=PDP−1Open formulaOpen in section