Let $A=\{a_1, a_2, a_3\}$ be a basis, of which each vector is aligned to a cartesian axis. Given a vector $v_{\langle A\rangle}$, how can I get transform it to the standard, canonical basis so it becomes $v_{\langle I\rangle}$?
I must apologize if this question is silly, I've completely forgotten my linear algebra classes (which makes me want to take them again).