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Linear Algebra

Exercise 6.11.13

Answers

Use the notation in that Lemma. We know that

W = ϕ_{β}^{- 1} (Z) = span {ϕ_{β}^{- 1} (x_{1}), ϕ_{β}^{- 1} (x_{2})} .

And compute that

T (ϕ_{β}^{- 1} (x_{i})) = ϕ_{β}^{- 1} (A x_{i}) \in ϕ_{β}^{- 1} (Z)

for $i = 1, 2$ . Hence $W$ is $T$ -invariant.

jephianlin

2011-06-27 00:00

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