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Let be a computed eigenvalue, and let
be its corresponding computed eigenvector.
For the simplicity of the presentation,
we normalize the computed eigenvector so that
The corresponding residual vector or
residual error is defined by
Ideally, we would like to have , but in practice .
It is conceivable that a small residual error implies
good accuracy in the computed and .
We are interested in knowing how accurate the computed
and are, given .