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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.

For a 1x1 matrix $[a]$, the determinant is simply the scalar entry $a$ itself.

Conditions: The matrix is of size 1x1.; The single entry is $a$.

For a 1x1 matrix $[a]$, the determinant is simply the scalar entry $a$ itself.

Conditions: The matrix is of size 1x1.; The single entry is $a$.