BASES, COORDINATES, LINEAR MAPS, AND MATRICES Math
... matrix CB B~ results in the coordinates of v relative to B. We know that if A is a matrix with n columns and if ej is the j th vector in the standard basis for Rn , then Aej is the jth column of A. Since [vj ] B = e j , equation (5) gives us (jth column of CB B~ ) = CB B~ ej = CB B~ [vj ] B = [vj ] ...
... matrix CB B~ results in the coordinates of v relative to B. We know that if A is a matrix with n columns and if ej is the j th vector in the standard basis for Rn , then Aej is the jth column of A. Since [vj ] B = e j , equation (5) gives us (jth column of CB B~ ) = CB B~ ej = CB B~ [vj ] B = [vj ] ...
