What would you like to understand?

Use the inverse of the change-of-basis matrix $P$. If $P$ converts from alternative to standard coordinates, then $P^{-1}$ converts from standard to alternative coordinates.

Conditions: The change-of-basis matrix $P$ is invertible.; The input vector is given in standard coordinates.

Use the inverse of the change-of-basis matrix $P$. If $P$ converts from alternative to standard coordinates, then $P^{-1}$ converts from standard to alternative coordinates.

Conditions: The change-of-basis matrix $P$ is invertible.; The input vector is given in standard coordinates.