An eigenvalue is a scalar $$\lambda$$ corresponding to an eigenvector $$v$$ of a square matrix $$A$$, which satisfies the equation $$Av = \lambda v$$.

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A vector $$v$$ is an eigenvector of a square matrix $$A$$ if and only if it is a nonzero vector for which multiplication by $$A$$ alters only the scale of $$v$$: $$Av = \lambda v$$.

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Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

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