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triangle-man committed Jul 19, 2024
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4 changes: 2 additions & 2 deletions exercises/axler-5a.md
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Expand Up @@ -80,11 +80,11 @@ $(T-\lambda I)v=0$ for some $v\neq 0$. Now consider applying
$S^{-1}(T-\lambda I)S$ to the vector $S^{-1}v$ (noting that $S$ is
invertible). We have
```math
\bigl(S^{-1}(T-\lambda I) \bigr) S^{-1)(v) = S^{-1}(T-\lambda I) v = 0.
\bigl(S^{-1}(T-\lambda I) \bigr) S^{-1}(v) = S^{-1}(T-\lambda I) v = 0.
```
On the other hand, we also have
```math
\bigl(S^{-1}(T-\lambda I) \bigr) S^{-1)(v) = (S^{-1}TS-\lambda I) (S^{-1}v),
\bigl(S^{-1}(T-\lambda I) \bigr) S^{-1}(v) = (S^{-1}TS-\lambda I) (S^{-1}v),
```
where, on the the right hand side, we have used $S^{-1}IS = I$.

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