Linear mapping/V over K/Trace/Definition

Trace (endomorphism)

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