Non-trivial eigenvectors of a 2*2 matrix in code [closed]

Question

Closed. This question needs details or clarity. It is not currently accepting answers.

---

Want to improve this question? Add details and clarify the problem by editing this post.

Closed 8 years ago.

Improve this question

I am trying to write a function in C which returns the eigenvalues and eigenvectors of a 2x2 matrix (looking for the eigen-values/vectors programatically). I've no problem with the eigenvalues which is fairly straightforward. But struggle with the eigenvectors, which is essentially solved by a system of simultaneous equations.

If I try a method such as: Solving a simultaneous equation through code this gives me a trivial solutions ([0,0]), as u=0 and v=0, in the case of eigenvectors.

eg. if my matrix is MAT = [[3,2],[2,1]], ie. a=3, b=2, c=2 and d=1, and u=0 and v=0, the equations suggested in the above link y = (v - uc/a) / (d - bc/a) and x = (uc/a - bc/a * y) / c, will equate to the solution [0,0], ie. the trivial solution.

Also, this seemingly provides an answer but I can't generate an example which agrees with the equations on: http://www.math.harvard.edu/archive/21b_fall_04/exhibits/2dmatrices/index.html

it also doesn't seem to cover all cases, what about the case when b and c are not equal to zero?

Answer 1

For the case of a 2x2 matrix, there is a simple analytical solution.

Your function should implement the solution presented at this link, with the three subcases. You may want to normalize the eigenvectors to unitary modulus as an additional step at the end.

Answer 2

Once you have the eigenvalues, the eigenvectors are easy to get.

I'd recommend an iterative method like Jacobi if your matrix is symmetric.