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Dimension of the space of skew-symmetric bilinear functions

smile

New member
Oct 15, 2013
19
Hello everyone,

I stuck on this problem:
find the dimension of the space of dimension of the space of skew-symmetric bilinear functions on $V$ if $dimV=n$.

I thought in this way, for skew-symmetric bilinear functions, $f(u,v)=-f(v,u)$, then the dimension will be $n/2$

Am I right?

thanks
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,492
Re: dimension of the space of skew-symmetric bilinear functions

I thought in this way, for skew-symmetric bilinear functions, $f(u,v)=-f(v,u)$, then the dimension will be $n/2$
Do you think the space of skew-symmetric functions is a fractal when $s$ is odd? :)
Suppose $(e_1,\dots,e_n)$ is a basis of $V$, $u=\sum_{i=1}^nx_ie_i$ and $v=\sum_{i=1}^ny_ie_i$. Expand $f(u,v)$ using linearity and skew symmetry. If $x_i$ and $y_i$ are fixed, how many parameters do you need to set to get a concrete number for $f(u,v)$?