Suppose the dielectric material is fixed in position and filling the capacitor, and you would have this term in the way of calculating something.
\int\nabla\cdot\left[\left(\Delta{D}\right){V}\right]{d}\tau
where D is the dielectric displacement
Now that turns into (by divergence...
Homework Statement
Let \mathrm{V} be a vector space. Determine all linear transformations \mathrm{T}:V\rightarrow V such that \mathrm{T}=\mathrm{T}^2.
Homework Equations
Hint was given and it was like this:
Note that x=\mathrm{T}(x)+(x-\mathrm{T}(x)) for every x in V, and show that...
The Problem:
Let S_{1} and S_{2} be subsets of a vector space V. Prove that span\left(S_{1}\cap S_{2}\right)\subseteq span\left(S_{1}\right)\cap span\left(S_{2}\right).
Give an example in which span\left(S_{1}\cap S_{2}\right) and span\left(S_{1}\right)\cap span\left(S_{2}\right) are equal and...