3
$\begingroup$

The eigenvectors ($\psi _i$) of the following matrix are rather complicated $$ \rho =\left( \begin{array}{cccc} G_+ & k & k & G_- \\ k & L_+ & L_- & k \\ k & L_- & L_+ & k \\ G_- & k & k & G_+ \\ \end{array} \right) $$ So, I want to suppose that $ E_i $ is the eigenvalue of $\rho$ that corresponding to the eigencfunction $\psi _i$, then to evaluate ($\psi _i$) as a function of $E_i $.

Is there a way I can do this with Mathematica?

Improve this question
$\endgroup$
1
  • $\begingroup$ Is your matrix purely symbolic? Or do the variables have numeric values? $\endgroup$
    – MikeY
    Jun 10, 2020 at 19:01

1 Answer 1

Reset to default
6
$\begingroup$

Assume your matrix is

ρ ={{p, k, k, m},
    {k, a, b, k},
    {k, b, a, k},
    {m, k, k, p}};

and you have found eigenvalues using

Eigenvalues[ρ]

And for some reason, you do not like Eigensystem. Then you can use the NullSpace command

NullSpace[ρ - (a - b) IdentityMatrix[4]]
NullSpace[ρ - (p - m) IdentityMatrix[4]]

to recover the eigenvectors corresponding to eigenvalues $E_1=a-b$, and $E_2=p-m$, etc.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.