###### Definition 4.1.1

Given a square \(n\times n\) matrix \(A\text{,}\) we say that a nonzero vector \(\vvec\) is an *eigenvector* of \(A\) if there is a scalar \(\lambda\) such that

\begin{equation*}
A\vvec = \lambda \vvec\text{.}
\end{equation*}

The scalar \(\lambda\) is called the *eigenvalue* associated to the eigenvector \(\vvec\text{.}\)