# Linear mapping/Diagonalizable/Eigenvectors/Definition

Diagonalizable mapping

Let denote a field, let denote a vector space, and let

denote a
linear mapping.
Then is called * diagonalizable*, if has a
basis
consisting of
eigenvectors
for .

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 ${}\varphi$.