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Exercise 5.4.38

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By Exercise 5.4.24, we already get the necessity. For the sufficiency, we may pick bases $β_{i}$ for $W_{i}$ such that $[T_{W_{i}}]$ is diagonal. Combining these bases to be a basis $β = ∪_{i = 1}^{k} β_{i}$ for $V$ . By using Theorem 5.25, we know that $T$ is diagonalizable.

jephianlin

2011-06-27 00:00

Exercise 5.4.38

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