Show that the matrices that are elements of $O ^ { + } ( 1,1 )$ are diagonalizable and find a matrix $P \in O ( 2 )$ such that, for every matrix $L \in O ^ { + } ( 1,1 )$, the matrix ${ } ^ { t } P L P$ is diagonal.
Show that the matrices that are elements of $O ^ { + } ( 1,1 )$ are diagonalizable and find a matrix $P \in O ( 2 )$ such that, for every matrix $L \in O ^ { + } ( 1,1 )$, the matrix ${ } ^ { t } P L P$ is diagonal.