This is a restatement of Exercise 6.4.36 in Assume that is an approximate eigenvalue for with corresponding approximate eigenvector 2. Form the residual let 2 and T Show that is an eigenpair...

This is a restatement of Exercise 6.4.36 in

Assume that
is an approximate eigenvalue for

with corresponding approximate eigenvector


₂
. Form the residual

let


₂
and

^T

Show that

is an eigenpair of

and

₂

Argue that

is an exact eigenpair of a matrix that is close to

Is

is a good approximate eigenpair of

in the sense of backward error