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text: 'Consider a linear transformation represented by a matrix $A$, and some vector $v$. If $Av = \\lambda v$, we say that $v$ is an _eigenvector_ of $A$ with corresponding eigenvalue $\\lambda$. Intuitively, this means that $A$ doesn't rotate or change the direction of $v$; it can only stretch it ($|\\lambda| > 1$) or squash it ($|\\lambda| < 1$) and maybe flip it ($\\lambda < 0$). While this notion may initially seem obscure, it turns out to have many useful applications, and many fundamental properties of a linear transformation can be characterized by its eigenvalues and eigenvectors.',
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