Kernel "stable under": is my interpretation correct?

In summary, "stable under" refers to a kernel's ability to remain consistent or unchanged when subject to a specific operation or condition. Its interpretation can vary depending on context and can affect performance. A kernel can be "stable under" multiple conditions and its stability is determined through mathematical analysis and testing.
  • #1
_Andreas
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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.​
 
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  • #2
I believe so. I can't think what else it would mean.
 
  • #3
Dick said:
I believe so. I can't think what else it would mean.

Ok, thanks!
 

1. What does it mean for a kernel to be "stable under" something?

"Stable under" refers to a property of the kernel that remains consistent or unchanged when subject to a certain operation or condition. For example, a kernel may be considered "stable under" a specific set of transformations or calculations.

2. Is my understanding of "stable under" correct?

It depends on your interpretation. "Stable under" can have different meanings depending on the context. It is best to clarify with the specific context in which it is being used.

3. How does the stability of a kernel affect its performance?

A kernel that is "stable under" certain operations may have better performance as it can be optimized for those specific operations. However, this is not always the case and other factors such as hardware and coding can also impact performance.

4. Can a kernel be "stable under" multiple conditions?

Yes, a kernel can be "stable under" multiple conditions. It is not limited to just one operation or condition.

5. How is the stability of a kernel determined?

The stability of a kernel is determined through mathematical analysis and testing. This involves evaluating the kernel's behavior under different operations and conditions to determine its stability.

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