# [✓] Get eigenvalues of a real symmetric matrix?

Posted 2 years ago
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 Hello,I am using Wolfram Alpha widgets for calculating Eigen values of a 3X3 real symmetric matrix. It is known the a real symmetric matrix has real Eigen values. However, the calculator is giving roots with iota (complex looking roots). So I have two questions,1) Are the Eigen values computed by the widget actually complex?2) If eigen values are not complex, then why aren't they simplified and given? How do I simplify them?The matrix which I used is : A = [ [ 1 2 3], [2 1 2], [3 2 3] ] Here is the link also, http://www.wolframalpha.com/widgets/view.jsp?id=9aa01caf50c9307e9dabe159c9068c41Thanks in advance. Hoping to hear from you soon.SandhyaP.S. : For the above matrix A, real Eigen values are 6.569, -1.342, -0.227.
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Posted 2 years ago
 It looks like the results are correct. For example, finding the numerical value of the first eigenvalue given shows it is real. In[5]:= 1/ 3 (5 + 55/(377 + 3 I Sqrt[2694])^(1/3) + (377 + 3 I Sqrt[2694])^( 1/3)) // N Out[5]= 6.56872 - 3.33067*10^-16 I