Unit Matrix is Proper Orthogonal
Jump to navigation
Jump to search
Theorem
The unit matrix $\mathbf I_n$ of order $n$ is proper orthogonal.
Proof
By Unit Matrix is Orthogonal, $\mathbf I_n$ is an orthogonal matrix.
By Determinant of Unit Matrix, the determinant of $\mathbf I_n$ is equal to $1$.
The result follows by definition of proper orthogonal.
$\blacksquare$