= Plücker embedding
{c}
{title2=$W=\operatorname{span}(u_1,\ldots,u_k)\mapsto[u_1\wedge\cdots\wedge u_k]$}
{wiki}
The <Plücker embedding> maps a $k$-plane to the projective class of the <exterior product> of a basis. A change of basis multiplies this product by its determinant, so the projective class is well defined. The plane is recovered as the vectors whose exterior product with this element is zero. For two-planes in $\mathbb C^4$, its image in $\mathbb{CP}^5$ is the <Klein quadric>.
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