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Let the $n\times n$ matrix $Z$ with $(i,j)$-element defined by $Z_{i,j}=i+j$. How to calculate the eigenvalue of $Z.$?

I have used Matlab to calculate it. I find no matter how bigger n is, there are always two nonzero eigenvalues. But how to get the formula for eigenvalues of $Z$?

iadvd
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Shine
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    See this question: http://math.stackexchange.com/questions/1261077/symmetric-matrix-eigenvalues/1261581#1261581 – Daniel May 05 '15 at 12:34

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