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Exercise 7.1.11

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By Theorem 7.7 and the assumption that the characteristic polynomial of $L_{A}$ splits, the transformation $L_{A}$ has a Jordan form $J$ and a corresponding Jordan canonical basis $β$ . Let $α$ be the standard basis for $𝔽^{n}$ . Then we have

J = {[L_{A}]}_{β} = {[I]}_{α}^{β} A {[I]}_{β}^{α}

and so $A$ is similar to $J$ .

jephianlin

2011-06-27 00:00

Exercise 7.1.11

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