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From Wikipedia

a linear operator T on a finite-dimensional vector space is semi-simple if every T-invariant subspace has a complementary T-invariant subspace.

I wonder if there is a concept for a linear operator to be simple? How is that defined?

Thanks!

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A linear operator $T$ is simple if there are no $T$-invariant subspaces except $V$ and $\{0\}$. So "semi-simple'' means "direct sum of simples." –  user29743 Nov 24 '12 at 20:06
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