Hello,

I want to write the following the matrix

0 $\displaystyle \beta $ 0

1 0 0

0 0 0

in the form $\displaystyle C^{-1}AC$

over $\displaystyle Mat(3,\mathbb{Q}(\sqrt{\beta}))$ and A is a diagonal matrix. I know that $\displaystyle \sqrt{\beta}\notin \mathbb{Q}$.

If there is a method to solve that kind of problem I would apperciate your help.

Thanks in advance.