Bivector and Existence of Basis

Sudharaka

Well-known member
MHB Math Helper
Hi everyone,

I am trying to find an approach to solve this but yet could not find a meaningful one. Hope you can give me a hint to solve this problem.

Problem:

Prove that for any bivector $$\epsilon\in\wedge^2(V)$$ there is a basis $$\{e_1,\,\cdots,\,e_n\}$$ of $$V$$ such that $$\epsilon=e_1\wedge e_2+e_3\wedge e_4+\cdots + e_{k-1}\wedge e_{k}$$.