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September 7th, 2018, 07:51 AM   #1
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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 10:07 PM.
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September 7th, 2018, 03:36 PM   #2
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A=i ??
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September 7th, 2018, 04:21 PM   #3
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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.
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