November 21st, 2017, 12:40 PM  #1 
Member Joined: Jan 2016 From: Blackpool Posts: 95 Thanks: 2  Matrix example
Find a matrix in $m_{2}(\mathbb{Q})$ such that the Eigen values do not belong in $\mathbb{Q}$

November 21st, 2017, 12:59 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,940 Thanks: 1006 
trivial $\begin{pmatrix}0 &2\\1 &0 \end{pmatrix}$ Eigenvalues $\pm \sqrt{2}$ 

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