9.11 Givens Rotation

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Givens Rotation

A Givens rotation is an $n \times n$ matrix of the form

Q (i, k, θ) = {[\begin{matrix} 1 & \dots & 0 & \dots & 0 & \dots & 0 \\ ⋮ & ⋱ & ⋮ & ⋮ & ⋮ \\ 0 & \dots & c & \dots & s & \dots & 0 \\ ⋮ & ⋮ & ⋱ & ⋮ & ⋮ \\ 0 & \dots & - s & \dots & c & \dots & 0 \\ ⋮ & ⋮ & ⋮ & ⋮ \\ 0 & \dots & 0 & \dots & 0 & \dots & 1 \end{matrix}]}_{n \times n}

The Givens rotation matrix has a total of $(n + 2)$ nonzero entries.

\begin{proof}
![[Note May 17, 2024.pdf]]

\end{proof}