2 like 0 dislike
380 views
Let $\vec{v}$ and $\vec{w}$ be vectors in $\mathbb{R}^{n}$. If $\|\vec{v}\|=\|\vec{w}\|$, show there is an orthogonal matrix $R$ with $R \vec{v}=\vec{w}$ and $R \vec{w}=\vec{v}$.
| 380 views

0 like 0 dislike
Let $R$ be an orthogonal matrix such that $R \vec{v}=\vec{w}$.

Then $R \vec{w}=R (R \vec{v})=R^2 \vec{v}=\vec{v}$.

Thus, $R$ is an orthogonal matrix with $R \vec{v}=\vec{w}$ and $R \vec{w}=\vec{v}$
by SIlver Status (12,174 points)

2 like 0 dislike
2 like 0 dislike
2 like 0 dislike
2 like 0 dislike
2 like 0 dislike
1 like 0 dislike
2 like 0 dislike
1 like 0 dislike
1 like 0 dislike