- Thread starter
- #1
- Feb 5, 2012
- 1,621
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 \(\epsilon=e_1\wedge e_2+e_3\wedge e_4+\cdots + e_{k-1}\wedge e_{k}\).
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 \(\epsilon=e_1\wedge e_2+e_3\wedge e_4+\cdots + e_{k-1}\wedge e_{k}\).