# [✓] 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. Answer
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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:= 1/ 3 (5 + 55/(377 + 3 I Sqrt)^(1/3) + (377 + 3 I Sqrt)^( 1/3)) // N Out= 6.56872 - 3.33067*10^-16 I Answer
Posted 2 years ago
 Mathematica tries to preserve infinite precision when it can. Use floating point numbers in your matrix like 1.0, 2.0 etc., and Eigenvalues will return numbers instead of expressions. Answer