Suppose I have a nondegenerate alternating bilinear form <,> on a vector space V. Under what conditions would a subspace U of V retain nondegeneracy? That is, if u ∈ U and u ≠ 0, then could I find a w ∈ U such that <u,w> ≠ 0?
So for example, it's clear that no one-dimensional subspace W of V...
A 25 uF and a 40 uF capacitor are charged by being connected across separate 50 V batteries. The capacitors are then disconnected from their batteries and connected to each other, with each negative plate connected to the other positive plate. What is the final charge on each capacitor, and what...