Givens rotation
= Givens rotation
{c}
{wiki}
A Givens rotation is the identity except for a coordinate-plane block
$$
\begin{pmatrix}c&s\\-s&c\end{pmatrix},
\qquad c^2+s^2=1.
$$
Choosing $(c,s)=(a,b)/\sqrt{a^2+b^2}$ maps the vector $(a,b)^T$ to $(\sqrt{a^2+b^2},0)^T$.