= Eigenpair
{title2=$(\lambda,v),\quad Av=\lambda v,\quad v\ne0$}
An eigenpair consists of an <eigenvalue> and a nonzero corresponding <eigenvector> of a specified <linear operator>. Scaling the <eigenvector> by a nonzero scalar gives another representation of the same eigendirection. For an approximate pair $(\widehat\lambda,\widehat v)$, its <eigenpair residual> is $A\widehat v-\widehat\lambda\widehat v$; a small residual alone need not give a small <eigenvector> error without spectral separation and conditioning information.
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