Let ##\{u^1,u^2,u^3,u^4\}## be a base of ##L##. If we take ##\sigma^1=u^1+u^2## and ##\sigma^2=u^3+u^4## then ##\sigma^1## and ##\sigma^2## are clearly vectors in ##L##, but if ##\alpha=\sigma^1\wedge\sigma^2## then ##\dim(M_\alpha)=1## and not ##2(=p)## as claimed by the text.
The ##\sigma##s...
Here's exercise 1 of chapter 2 in Flanders' book.
Let ##L## be an ##n##-dimensional space. For each ##p##-vector ##\alpha\neq0## we let ##M_\alpha## be the subspace of ##L## consisting of all vectors ##\sigma## satisfying ##\alpha\wedge\sigma=0##. Prove that ##\dim(M_\alpha)\leq p##. Prove also...
I wasn't sure whether my formula for ##*\lambda## was correct. I had doubts because I got a wrong sign in example 1 on page 16. That example says that if the base of ##V## is ##(dx^1,dx^2,dx^3,dt)## where ##(dx^i,dx^i)=1## and ##(dt,dt)=-1##, then $$
*(dx^i dt) = dx^j dx^k,
$$ where...
I'm reading section 2.7 of Flanders' book about differential forms, but I have some doubts.
Let ##\lambda## be a ##p##-vector in ##\bigwedge^p V## and let ##\sigma^1,\ldots,\sigma^n## be a basis of ##V##. There's a unique ##*\lambda## such that, for all ##\mu\in \bigwedge^{n-p}##,$$
\lambda...