Finding eigenvector when rref returned is identity
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I'm computing some eigenvalues and eigenvectors.
λ
What does it mean, when taking a found eigenvalue
x
and trying to find its corresponding eigenvector
λx−Ax=0
(from the equality
) reduces to identity matrix?
Here
λ
it's claimed that it means that eigenvalue
is not an eigenvalue. But how is that reasonable? Or is it possible that eigenvalues can be rejected, even after they were found as solutions to the characteristic polynomial?
λ
What does it mean, when taking a found eigenvalue
x
and trying to find its corresponding eigenvector
λx−Ax=0
(from the equality
) reduces to identity matrix?
Here
λ
it's claimed that it means that eigenvalue
is not an eigenvalue. But how is that reasonable? Or is it possible that eigenvalues can be rejected, even after they were found as solutions to the characteristic polynomial?
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