Linear mapping/V over K/Trace/Definition

Let ${\displaystyle {}K}$ be a field, and let ${\displaystyle {}V}$ denote a finite-dimensional ${\displaystyle {}K}$-vector space. Let ${\displaystyle {}\varphi \colon V\rightarrow V}$ be a linear mapping, which is described by the matrix ${\displaystyle {}M}$ with respect to a basis. Then ${\displaystyle {}\operatorname {trace} {\left(M\right)}}$ is called the trace of ${\displaystyle {}\varphi }$, written as ${\displaystyle {}\operatorname {trace} {\left(\varphi \right)}}$.