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Linear algebra is one of the more well-behaving parts of math. Yet, I wonder if there occur any pathologies in finite-dimensional linear algebra?

By a pathology I mean a phenomenon whose properties are considered atypically bad or counterintuitive, see Wikipedia.

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    Isn't that a bit a matter f taste? Some might consider things like the zero-dimensional space of $0\times 0$ matrices pathological ...2012-11-15
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    Community wiki?2012-11-16

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