# Finding eigenvectors with given set of eigenvalues [duplicate]

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?

• "miserably failed"? Eigensystem[{{0, k1, k2}, {k1, 0, k3}, {k2, k3, 0}}] // ToRadicals – KraZug May 15 '17 at 8:57
• Try to make it answer. Thanks @KraZug – L.K. May 15 '17 at 8:59
• I suspect that the question should be closed actually. – KraZug May 15 '17 at 9:02

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