Linear mapping/Diagonalizable/Eigenvectors/Definition

Diagonalizable mapping

Let ${}K$ denote a field, let ${}V$ denote a vector space, and let

$\varphi \colon V\longrightarrow V$

denote a linear mapping. Then ${}\varphi$ is called diagonalizable, if ${}V$ has a basis consisting of eigenvectors for ${}\varphi$.