(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

T: R_{3}[x] R_{3}[x] // for some reason the arrow symbol isn't working! When I do the arrow it previews as the third power for some reason. Also, whenever I preview post, it adds12 b[3] again for some reason and I have to delete those lines every time...a bit fustrating...

T(1) = 3 + 2x +4X^{2}

T(x) = 2 + 2x^{2}

T(x^{2}) = 4 + 2x 3x^{2}

Find all eigenvalues and their linear subspaces they create.

3. The attempt at a solution

I don't exactly understand what to do here. I am used to transformations from R^{3}to R^{3}, not the polynomial transformations. And I am a bit confused how they wrote T(1) T(x) and T(x^{2}) separately. Is that the way you write the transformations for polynomials? I thought it should be like this: T(alpha_{0}+ alpha_{1}x + alpha_{2}x^{2}) = (.....)

I guess I just need someone to explain what

T(1) = 3 + 2x +4X^{2}

T(x) = 2 + 2x^{2}

T(x^{2}) = 4 + 2x 3x^{2}

means.

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Eigenvalues and their spaces

**Physics Forums | Science Articles, Homework Help, Discussion**