Generalized eigenspace invariant?

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SUMMARY

The discussion centers on the concept of generalized eigenspaces and their invariance under a linear operator T in finite-dimensional vector spaces over the complex numbers. The generalized eigenspace for an eigenvalue y is defined as the set of all vectors v in V such that there exists a j ≥ 1 for which (T - yI)^j(v) = 0. The term "invariant" in this context refers to the property that the generalized eigenspace remains unchanged under the action of the operator T.

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mind0nmath
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Hey,
Is the generalized eigenspace invariant under the operator T? Let T be finite dimensional Linear operator on C(complex numbers).
My understanding of the Generalized Eigenspace for the eigenvalue y is:
"All v in V such that there exists a j>=1, (T-yIdenitity)^j (v) = 0." plus 0.
thanks
 
Physics news on Phys.org
What does invariant mean? Try to prove it.
 
got it. thanks.
 

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