what symbol is used for linear operator actions?


by sunjin09
Tags: actions, linear, operator, symbol
sunjin09
sunjin09 is offline
#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?
Phys.Org News Partner Mathematics news on Phys.org
Hyperbolic homogeneous polynomials, oh my!
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
mathman
mathman is offline
#2
May2-12, 03:33 PM
Sci Advisor
P: 5,942
G(v) is fine.
sunjin09
sunjin09 is offline
#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
micromass is online now
#4
May2-12, 10:52 PM
Mentor
micromass's Avatar
P: 16,692

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
sunjin09 is offline
#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
sunjin09 is offline
#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!


Register to reply

Related Discussions
Operator Calculus Symbol Question Calculus 0
Verify that any square matrix is a linear operator when considered as a linear map. Calculus & Beyond Homework 3
a Binary Operator Symbol Identification. Differential Geometry 1
Linear Algebra, Adjoint of a Linear Operator and Inner Product Spaces Calculus & Beyond Homework 2
a Square as a mathematical symbol/operator Math & Science Software 3