I am given a matrix. I would like to reduce it to its upper Hessenberg Form. We are discussing eigenvalue computations in Numerical Analysis and the textbook just gives the algorithm for it without an example. So I was wondering if anyone knew of any textbook or an article or a forum where it is shown how to transform a given matrix $A$ into its upper Hessenberg form with as much detail as possible. Or if someone could show me the steps, that would be fantastic as well. The example that is given in the book is as follows. Thanks!
$$ \begin{pmatrix} 4 & 2 & 2 & 1 \\ 2 & 1 & 3 & 0 \\ 2 & 3 & 1 & 1 \\ 1 & 0 & 1 & 1 \\ \end{pmatrix} $$