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[✓] Get eigenvalues of a real symmetric matrix?

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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=9aa01caf50c9307e9dabe159c9068c41

Thanks in advance. Hoping to hear from you soon.

Sandhya

P.S. : For the above matrix A, real Eigen values are 6.569, -1.342, -0.227.

POSTED BY: Sandhya Tripathi
Answer
6 months 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
POSTED BY: Frank Kampas
Answer
6 months 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.

POSTED BY: Ken Mednick
Answer
1 month ago

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