Givens rotation of the following vector of 3 elements.

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Yes, I was right, the matrix is a correct Givens Rotation Matrix that respects the required transformation.

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Mihai Alin
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Mihai Alin

Updated on August 01, 2022

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  • Mihai Alin
    Mihai Alin over 1 year

    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?

    • Mihai Alin
      Mihai Alin almost 10 years
      @user127001 thank you, I'm new to math.stackchange.com :D