Wedge product and vectors

Hello,

i want to proof this claim:

Let V be a finite vector space.

are not linearly indipendent <=> .

One direction(=>) wasn't so difficult. But i have problems with the other direction.

So we have .

Can you see, why they have to be linearly dependent?

Regards

Re: Wedge product and vectors

The (<=) direction can be proven by observing that is the linear form that corresponds to (a multiple of) the determinant of when expressed for a given basis.

Re: Wedge product and vectors

Quote:

Originally Posted by

**TheArtofSymmetry** Just wondering, how do you derive this?

?

Their determinant.