Kernel "stable under": is my interpretation correct?

[_Andreas]

[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.​

 

[Dick]

I believe so. I can't think what else it would mean.

 

[_Andreas]

I believe so. I can't think what else it would mean.

Ok, thanks!