Testing Eigen Values: How to Check Accuracy Before Finding Eigen Vectors

[cragar]

Homework Statement

This is probably a really simple question , but how do i test my eigen values to see if there right ,---------- (A-tI)x=0 where t is an eigen value , I know how to test if my eigen vectors are correct but how do i test to see if my eigen values are right , before i find my eigen vectors.

 

[radou]

Well, if you solved your characteristic equation correct, then your eigenvalues should be correct. I don't know how you could check them before solving the eigenvalue problem and using the eigenvectors. Eigenvalues have some certain properties, but I don't see how they could help you determine if you're right.

 

[Matterwave]

I think you're going to have to calculate the Eigenvectors and then check to see if they are both right.

Otherwise, you can check your answers using a calculus-enabled program like Maple.

 

[cragar]

ok thanks , so when i find my eigen values and eigen vectors i can use
Ax=tx to see if they are both right .

 

[radou]

Not than you can, you have to use it. :)

 

[Jakesaccount]

Well there's any number of things you can do. First of all you should multiply your matrix with your eigenvector and see if the vector you get is parallel to the eigenvector.

Then the trace of the matrix should be the sum of the eigenvalues, so you can check that also. Then the determinant of the matrix should be the product of the eigenvalues, check that if you have a reasonably small matrix.