what symbol is used for linear operator actions?

sunjin09

Given a vector v[itex]\in H[/itex]: R2->R3 which is a function from R2 to R3, and an operator G: H->H on the space H in which v lives, what is the most commonly used symbol to refer to this mapping, i.e., G(v)=G[itex]\otimes v[/itex] or something else?

mathman

G(v) is fine.

sunjin09

Thank you for replying, but I want to emphasize that G is a 3x3 matrix valued operator that multiplies the 3x1 vector valued function v then integrated over the entire domain, is the tensor product [itex]\otimes[/itex] appropriate? I used a dot but was complained about by the reviewer.

micromass

The tensor product is not appropriate, neither is the dot. Using G(v) makes most sense. Is there a reason why you don't want to use G(v)?

sunjin09

Thanks again for clarifying, I guess I just wanted to emphasize the matrix vector multiplication part, I'll use G(v) so that there's no ambiguity. One more question though, if I apply G n times to v, n>=0, is [itex]G^n(v)[/itex] appropriate?

sunjin09

I found the notation G^n(v)=G(G(G...G(v)...)) in a textbook. Thank you both!