Linear mapping/Field/Isomorphism/Definition

Let ${\displaystyle {}K}$ denote a field, and let ${\displaystyle {}V}$ and ${\displaystyle {}W}$ denote ${\displaystyle {}K}$-vector spaces. A bijective linear mapping

${\displaystyle \varphi \colon V\longrightarrow W}$

is called an isomorphism.