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Exercise 7.1.5

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If $x$ is an element of in two cycles, which is said to be $γ_{1}$ and $γ_{2}$ without loss of generality, we may find the smallest integer $q$ such that

{(T - λI)}^{q} (x) = 0 .

This means that the initial eigenvectors of $γ_{1}$ and $γ_{2}$ are both ${(T - λI)}^{q - 1} (x)$ . This is a contradiction. Hence all cycles are disjoint.

jephianlin

2011-06-27 00:00

Exercise 7.1.5

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