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 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 three-dimensional 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 ?? Thanks from romsek 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. Thanks from topsquark Tags algebra, calculus, form, operator, vector Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post abc98 Algebra 10 September 20th, 2015 06:49 PM PerfectTangent Algebra 2 February 25th, 2014 10:18 PM soumita Linear Algebra 4 April 25th, 2013 01:15 PM balbasur Algebra 3 July 18th, 2010 07:12 PM Wojciech_B Linear Algebra 0 December 7th, 2009 02:52 PM

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