# Linear mapping/Eigenvector/Definition

Eigenvector

Let be a field, a -vector space and

a
linear mapping.
Then an element
, ,
is called an * eigenvector* of
(for the
eigenvalue
),
if

for some holds.

Eigenvector

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

- $\varphi \colon V\longrightarrow V$

a
linear mapping.
Then an element
${}v\in V$, ${}v\neq 0$,
is called an * eigenvector* of ${}\varphi$
(for the
eigenvalue
${}\lambda$),
if

- ${}\varphi (v)=\lambda v\,$

for some ${}\lambda \in K$ holds.