Field trace
In mathematics, the field trace is a particular function defined with respect to a finite field extension L/K, which is a K-linear map from L onto K. == Definition == Let K be a field and L a finite extension (and hence an algebraic extension) of K. L can be viewed as a vector space over K. Multiplication by α, an element of L, m α : L → L given by m α ( x ) = α x {\displaystyle m_{\alpha }:L\to L{\text{ given by }}m_{\alpha }(x)=\alpha x} , is a K-linear transformation of this vector space into itself. The trace, TrL/K(α), is defined as the trace (in the linear algebra sense) of this linear transformation.