I have encountered a task, which I do not really know how to approach.
I need to find a decomposition
$$A = U\Sigma V^T$$
of the matrix:
$$ A = \begin{pmatrix} 2&1&2&\\ -2&-1&-2&\\ 4&2&4&\\ 2&1&2&\\ \end{pmatrix} $$
Where $\Sigma$ is a rect diagonal matrix of size 4 x 3, U and V are orthogonal matrices, and the upper right element of V is equal to $1\sqrt2$.
Thank you in advance!