(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that W is a T-invariant subspace of T for:

W = E[tex]_{\lambda}[/tex]

2. Relevant equations

3. The attempt at a solution

Ok, so I know that I need to show that T maps every element in E[tex]_{\lambda}[/tex] to .

E[tex]_{\lambda}[/tex] = N(T-[tex]\lambda[/tex]I)

so T must map every eigenvector related to [tex]\lambda[/tex] to another eigenvector in E[tex]_{\lambda}[/tex]

T(x) maps to zero vector, when x is an eigenvector associated with [tex]\lambda[/tex] which is in the eigenspace of [tex]\lambda[/tex], correct?

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# Homework Help: T-Invariant Subspaces

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