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[tex]A-\lambda I=\begin{pmatrix}4 & 1 \\ 4 & 1\end{pmatrix}[/tex]

You could write the eigenvector as:

[tex]\operatorname{span}\begin{pmatrix}1 \\ -4\end{pmatrix}[/tex]

My question is: does it matter how you write the "span" part of it?

For instance, would [tex]\operatorname{span}\begin{pmatrix}-1 \\ 4\end{pmatrix}[/tex] be preferred (or different) than what I have above?

Thanks for your help.