Dual mapping/Rank/Exercise

Let

$\varphi \colon V\longrightarrow W$

be a linear mapping between the finite-dimensional ${}K$-vector spaces ${}V$ and ${}W$, and let

$\varphi ^{*}\colon {W}^{*}\longrightarrow {V}^{*}$

be the dual mapping. Show

${}\operatorname {rk} \,\varphi =\operatorname {rk} \,\varphi ^{*}\,.$

Create a solution