Kernel "stable under": is my interpretation correct?

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SUMMARY

The discussion clarifies the interpretation of the term "stable under" in the context of endomorphisms A1, A2, A3, ..., Ar. Specifically, it confirms that if W is the kernel of Ar - λI (where λ is an eigenvalue), then W is indeed stable under the previous endomorphisms A1, A2, ..., Ar-1. This means that for any element u in W, the transformation Aku remains in W, establishing that "stable under" is equivalent to "closed under" in this context.

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[SOLVED] Kernel "stable under": is my interpretation correct?

Homework Statement



A1, A2, A3,..., Ar are endomorphisms. W is the kernel of Ar - lambda*I, where lambda is the eigenvalue of Ar. W is stable under A1, A2, A3,..., Ar-1. Question: does "stable under" equal "closed under", and is the following interpretation of this stability correct?

For all elements u in W, Aku is an element in W.​
 
Last edited:
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I believe so. I can't think what else it would mean.
 
Dick said:
I believe so. I can't think what else it would mean.

Ok, thanks!
 

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