Tagged Questions

0
votes
1answer
51 views

Prove that D (the differential operator) maps V (a vector space) into V.

I'm quite confused about what "into" means here and, more importantly, how I am supposed to prove that something maps a vector space into (not onto) another vector space. Here's some of the ...
1
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2answers
105 views

Transpose of the differential operator

Is the differential operator ${d\over dx}$ antisymmetric? If so, what does it even mean to take it's transpose? Thank you.
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0answers
65 views

diagonalizing a simple matrix of differential operators

I have the following endomorphism (whose determinant I would like to calculate) of the (infinite dimensional) vector space $\Omega^0(M) \oplus \Omega^1(M)$ for some closed Riemannian manifold $M$: ...
1
vote
1answer
122 views

Differentiation operator applying on matrix

I need to apply a differential operator (nabla) on a matrix. Problem is, that I don't know how to calculate that. Do I treat nabla as a column vector and simply multiply vector with the matrix? Or is ...