Thread: Need some clarification on eigenvalues/eigenvectors

i have a quick question about eigenvalue/eigenvectors

so say i have a matrix

-3 0
2 -1

with eigen values -1 and -3 (i'm pretty sure they are right)

so for the first eigenvalue (-1) i get a matrix

-2 0
2 0

and for the second (-3)

0 0
2 2

well i not realy sure how to get the eigen vector from these?...wondering if someone could help me...this would really help, thanks

Originally Posted by action259

i have a quick question about eigenvalue/eigenvectors

so say i have a matrix

-3 0
2 -1

with eigen values -1 and -3 (i'm pretty sure they are right)

so for the first eigenvalue (-1) i get a matrix

-2 0
2 0

and for the second (-3)

0 0
2 2

well i not realy sure how to get the eigen vector from these?...wondering if someone could help me...this would really help, thanks

You have the eigenvalues right, but what is this matrix associated with the eigenvalue? I've never heard of it. Anyway, to get the eigenvectors:

:

Let the eigenvector be

So:




Thus or a = 0, and which says that , leaving b undetermined. So the eigenvector for is of the form

where b is undetermined.

You can use the same method to get the eigenvector for .

-Dan

The characteristic polynomial is your friend; you'll use it a lot. That is,

Ax = (lambda)x --> (A - (lamdba)(I))x = 0, where I is the identity matrix.