- Thread starter
- #26

- Apr 14, 2013

- 4,713

Ok, but shouldn't these vectors be then the first and second column of $D$? How do we get then the cosine and the sine?Let's assume for now that $v$ is independent from $w$.

And let $b_3$ and $b_4$ be vectors that are orthogonal to both $v$ and $w$.

Then we have that $\sigma_v(v)=-v$, so the first column of the matrix of ${\sigma_v}$ with respect to the basis $(v,w,b_3,b_4)$ is $\begin{pmatrix}-1\\0\\0\\0\end{pmatrix}$.

We also have that $\sigma_w(w)=-w$, so the second column of he matrix of ${\sigma_w}$ with respect to the basis $(v,w,b_3,b_4)$ is $\begin{pmatrix}0\\-1\\0\\0\end{pmatrix}$.