TITLE: Do non-square matrices have eigenvalues?
QUESTION [44 upvotes]: I've looked at this and it doesn't help because I don't know anything about SVD. Can someone dumb it down for me please?

REPLY [29 votes]: Eigenvalues and eigenvectors of a matrix, say $A$, help us find subspaces which are invariant under $A$ (when $A$ is seen as a linear transformation). If $A$ is non-square, then $A:\mathbb{R}^m\rightarrow \mathbb{R}^n$, where $m\neq n$. Hence $Av=\lambda v$ makes no sense, since $Av\notin\mathbb{R}^m$.
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