Linear mapping/Finite dimensional/Eigenvalues bounded by dimension/Fact/Proof/Exercise

Let ${}K$ be a field, ${}V$ a finite-dimensional ${}K$-vector space and

$\varphi \colon V\longrightarrow V$

a linear mapping. Show that there exist at most ${}\dim _{K}{\left(V\right)}$ many eigenvalues for ${}\varphi$.

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