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

For each linear operator T, find a basis for each generalized eigenspace of T consisting of a union of disjoint cycles of generalized eigenvectors. The find a Jordan canonical formJof T.

a) T is the linear operator on P_{2}(R) defined by T(f(x)) = 2f(x) - f '(x)

2. Relevant equations

3. The attempt at a solution

OK, so I know the matrix rep of this transformation on the standard basis {1, x, x^{2}}:

T(1) = 2

T(x) = -1 + 2x

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

[tex][T]_{\beta}[/tex] =

2 -1 0

0 2 -2

0 0 2 and the eigenvalue of this matrix is [tex]\lambda[/tex] = 2 with a multiplicity of 3.

I know the JOrdan form will be :

2 1 0

0 2 1

0 0 2 , just not sure how to get the basis or how to get the J from the [T]

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# Homework Help: Generalized Eigenspace and JOrdan Form

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