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This question already has an answer here:

I have a matrix whose eigenvalues I was trying calculate. Mathematica miserably failed in calculating the eigenvalues. So, I calculated them manually. But can I use it to find eigenvalues, atleast.

Hg = ( {
    {0, k1, k2},
    {k1, 0, k3},
    {k2, k3, 0}} );

But let us say, I have l1, l2 and l3 as my eigenvalues. Can I find the eigenvectors? Can I get the eigennvalues for this symbolic matrix?

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marked as duplicate by J. M. is away May 17 '17 at 11:40

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    $\begingroup$ "miserably failed"? Eigensystem[{{0, k1, k2}, {k1, 0, k3}, {k2, k3, 0}}] // ToRadicals $\endgroup$ – KraZug May 15 '17 at 8:57
  • $\begingroup$ Try to make it answer. Thanks @KraZug $\endgroup$ – L.K. May 15 '17 at 8:59
  • $\begingroup$ I suspect that the question should be closed actually. $\endgroup$ – KraZug May 15 '17 at 9:02
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Eigensystem or Eigenvalues will give answers in terms of Root expressions for non-numerical values, you can force them to give radicals (when they are degree <5) with ToRadicals.

Eigensystem[{{0, k1, k2}, {k1, 0, k3}, {k2, k3, 0}}] // ToRadicals

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