September 7th, 2018, 08:51 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 11:07 PM. 
September 7th, 2018, 04:36 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,855 Thanks: 744 
A=i ??

September 7th, 2018, 05:21 PM  #3 
Senior Member Joined: Sep 2016 From: USA Posts: 684 Thanks: 459 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 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Help converting standard form of quadratic function to vertex form  abc98  Algebra  10  September 20th, 2015 06:49 PM 
Converting Quadratics from standard form to Vertex form  PerfectTangent  Algebra  2  February 25th, 2014 10:18 PM 
Finding basis for an operator of particular form  soumita  Linear Algebra  4  April 25th, 2013 01:15 PM 
How to find polar form and cartesian form of th......  balbasur  Algebra  3  July 18th, 2010 07:12 PM 
normal form for real quadratic form  Wojciech_B  Linear Algebra  0  December 7th, 2009 02:52 PM 