September 7th, 2018, 07:51 AM  #1 
Newbie Joined: Sep 2018 From: Maroc Posts: 1 Thanks: 0  Form of an operator
Please help with this problem. Let x be a vector in a threedimensional space R^3 and c be a constant vector and let A be an operator acting on R^3 with values in R^3, then I'm looking for the form of the operator A such that A(x + c) = c + A^2(x) Thank you for your reply. Last edited by skipjack; September 7th, 2018 at 10:07 PM. 
September 7th, 2018, 03:36 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,710 Thanks: 675 
A=i ??

September 7th, 2018, 04:21 PM  #3 
Senior Member Joined: Sep 2016 From: USA Posts: 578 Thanks: 345 Math Focus: Dynamical systems, analytic function theory, numerics 
Do you mean linear operator? If so there seems to be 3 possibilities. Maybe more since I'm probably missing something. 1. $c = 0$ means $Ax = A^2(x)$. Then either $x$ is an eigenvector for $A$ or $x \in$ ker$(A)$. 2. $c$ and $x$ are linearly dependent and both are eigenvectors for $A$. 3. $c$ and $x$ are linearly independent. Nothing can really be concluded here. 

Tags 
algebra, calculus, form, operator, vector 
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