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In the given matrix, only one eigen value is real. What is that eigen value ?

\begin{bmatrix} 1& 5& 4& 3& 2\\ 2& 1& 5& 4& 3\\ 3& 2& 1& 5& 4\\ 4& 3& 2& 1& 5\\ 5& 4& 3& 2& 1 \end{bmatrix}

Is there any small approach ?

Jon Garrick
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    @Moo, it just completely amazes me how some people can just pull up some obscure result like that so quickly. – Decaf-Math Feb 06 '17 at 19:02
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    Observe that the totals of the rows/columns are all equal. Act then by the matrix at the vector $x=(1,1,1,1,1)^T.$ You'll see that $Ax=15x,$ and so 15 is a real eigenvalue. – Olod Feb 06 '17 at 19:03

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