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hitmeoff
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Homework Statement
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 form J of T.
a) T is the linear operator on P2(R) defined by T(f(x)) = 2f(x) - f '(x)
Homework Equations
The Attempt at a Solution
OK, so I know the matrix rep of this transformation on the standard basis {1, x, x2}:
T(1) = 2
T(x) = -1 + 2x
T(x2) = -2x + 2x2
[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]