Finding Eigenvectors and Values of Non-Hermitian Matrices with Mathematica

[physicsjock]

Hey,

I have two quick questions,

Does mathematica automatically find the eigenvectors and values when you find the eigensystem of a non-Hermitian matrix?

I've been searching the net trying to find a way to find these vectors/values but everything I find briefly touches upon non-Hermitian without actually doing anything.

The method I have been trying is to apply the householder transformation and turn the matrix into a upper triangular hessian matrix, but after 10 applications of the householder transformation my matrix doesn't show any signs of change.

Could anyone point me in the right direction in finding the eigevectors and values of a non-Hermitian matrix?

Also if anyone knows if mathematica actually does properly determine these quantities of non-Hermitian matrix automatically when running eigensystem please let me know.

This line of code is the only part I'm not sure about, I have a feeling that mathematica doesn't determine the eigensystem of non-Hermitians properly.


Thanks in advanced

 

[Daniiel]

I've never actually seen an example of this before,

Try "They algebraic eigenvalue problem" by J.H.Wilkinson