Talk:Linear complex structure

From Wikipedia, the free encyclopedia

It seems to me that there ought to be something in here, say, in the section on preserving other structures, that given a real inner product g on V, we can induce a Hermitean inner product on (V, J) via the rule h(v, w) = g(v, w) + ig(Jv, w). This then satisfies h(v, v) = g(v, v), h(iv, w) = ih(v, w), and h(v, w) = h(w, v)* Rwilsker 17:24, 24 July 2007 (UTC)

currently there's something, right? Commentor (talk) 05:03, 23 March 2008 (UTC)

Quote: "In general, if a vector space U admits a decompositon U = S ⊕ T then the exterior powers of U can be decomposed as follows: \Lambda^r U = \bigoplus_{p+q=r}(\Lambda^p S)\otimes(\Lambda^q T)." Can somebody comment on this? Why is it true? Let U = R3,S = R2,T = R1,r = 2. Then the space of antisymmetric 2-forms on U is 3-dimensional, yet the expression on the right-hand side gives only one dimension. Should one raise the right hand side to the appropriate binomial coefficient? Commentor (talk) 05:03, 23 March 2008 (UTC)