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,
Thanks in advance. Hoping to hear from you soon.
P.S. : For the above matrix A, real Eigen values are 6.569, -1.342, -0.227.
It looks like the results are correct. For example, finding the numerical value of the first eigenvalue given shows it is real.
3 (5 + 55/(377 + 3 I Sqrt)^(1/3) + (377 + 3 I Sqrt)^(
1/3)) // N
Out= 6.56872 - 3.33067*10^-16 I
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.