1
$\begingroup$

Prove that, if $T$ is an orthogonal transformation on $\mathbb R^2$ such that $\det T = -1$, there exists an orthonormal basis for $\mathbb R^2$ such that the matrix of $T$ with respect to this basis is

$$ \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}. $$

  • 1
    What have you tried? Do you know what an orthogonal transformation is? If yes, can you please include the definition in your question? Thank you.2012-10-14
  • 1
    What properties do orthogonal matrices have with regards to diagonalization? What must the diagonal entries be? Why can't T be a rotation?2012-10-14

2 Answers 2