Let $B$ be a linear transformation. If we found an invarient subspace say $W$ under B, does this follow that $W$ is subset of some eigenspace of $B$ ?
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No, since the ambient space itself is invariant. – Bernard Jun 07 '17 at 08:16
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Okay.But can I at least find an eigenvector of $B$ in $W$ ? – emelie Jun 07 '17 at 08:30
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Yes, if the characteristic polynomial of the restriction of $B$ to $W$ has roots in the base field (I suppose you're working with finite dimensional spaces). – Bernard Jun 07 '17 at 08:32
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Yes, I am. Thank you – emelie Jun 07 '17 at 08:37