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What symbol is used for linear operator actions?

by sunjin09
Tags: actions, linear, operator, symbol
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sunjin09
#1
May2-12, 02:31 PM
P: 312
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?
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mathman
#2
May2-12, 03:33 PM
Sci Advisor
P: 6,038
G(v) is fine.
sunjin09
#3
May2-12, 07:25 PM
P: 312
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
#4
May2-12, 10:52 PM
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What symbol is used for linear operator actions?

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
#5
May3-12, 01:32 PM
P: 312
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
#6
May3-12, 03:32 PM
P: 312
I found the notation G^n(v)=G(G(G...G(v)...)) in a textbook. Thank you both!


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