###### Definition4.1.1

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 $$\vvec\text{.}$$

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