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Exercise 5.A.5

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Proof. Suppose $U_{1}, \dots, U_{m}$ are subspaces of $V$ invariant under $T$ . Let $u \in U_{1} \cap \dots \cap U_{m}$ . For each $j = 1, \dots, m$ , because $U_{j}$ is invariant under $T$ and $u \in U_{j}$ , it follows that $Tu \in U_{j}$ . Therefore $Tu \in U_{1} \cap \dots \cap U_{m}$ . □

celiopassos

2017-10-06 00:00

Exercise 5.A.5

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