Semi-simple operator

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

An important result regarding semi-simple operators is that, a linear operator on a finite dimensional vector space over an algebraically closed field is semi-simple if and only if it is diagonalizable.

[edit] References

• Kenneth Hoffman and Ray Kunze. "Semi-Simple operators". Linear Algebra: pp. 262-265, Pearson Education. ISBN 81-297-0213-4.