I have to find the givens rotation matrix that will transform the following vector $[1, 1, -1]^T$ to $[y, 1, 0]^T$ (basically to insert a $0$ on the third position without altering the second one).
I tried to solve this problem but I'm not sure I am correct. My approach was the following:
$$\begin{bmatrix}
c & 0 & -s\\
0 & 1 & 0 \\
s & 0 & c
\end{bmatrix}\cdot
\begin{bmatrix}1\\1\\-1
\end{bmatrix}=
\begin{bmatrix}
y\\1\\0
\end{bmatrix}$$
So I have the following equation set:
$$c – s = y \text{ and }s – c = 0 $$
Which means that s = c so, theta angle is 45 degrees meaning that the Givens matrix for that rotation its the following:
$$\begin{bmatrix}
√2/2 & 0 & -√2/2\\
0 & 1 & 0 \\
√2/2 & 0 & √2/2
\end{bmatrix}$$
Am I right?
Best Answer
Yes, I was right, the matrix is a correct Givens Rotation Matrix that respects the required transformation.