I have a question about this theorem.(adsbygoogle = window.adsbygoogle || []).push({});

Let V be an n-dimensional inner product space, and let T:V-->V be an orthogonal linear transformation. Let S be a minimal invariant subspace under T. Then S is one dimensional or two dimensional.

I understand what this theorem says and I follow the proof given in my book, but I can't see any reason why the hypothesis that T be orthogonal is necessary.

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# Minimal invariant subspaces

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