Let V = Mat n ( K ) {\displaystyle {}V=\operatorname {Mat} _{n}(K)} be the space of the n × n {\displaystyle {}n\times n} -matrices over the field K {\displaystyle {}K} , with the standard basis e i j {\displaystyle {}e_{ij}} . Describe the trace as a linear combination with respect to the dual basis e i j ∗ {\displaystyle {}e_{ij}^{*}} .
