- #1
hitmeoff
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Homework Statement
Show that W is a T-invariant subspace of T for:
W = E[tex]_{\lambda}[/tex]
Homework Equations
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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