Tensor product/Wedge product/Fact/Proof

Proof

The multilinear mapping

$V^k⟶\stackrel{k}{\bigwedge }V,(v_1,\dots ,v_k)⟼v_1\wedge \dots \wedge v_k,$

induces, due to fact  (2), the linear mapping. The surjectivity rests on the fact that the generating system $v_1\wedge \dots \wedge v_k$ belongs to the image.

To fact