Semi-simple operator

Semi-simple operator

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.

References

*cite conference | author=Kenneth Hoffman and Ray Kunze | title=Semi-Simple operators | booktitle=Linear Algebra|publisher=Pearson Education| pages=pp. 262-265|id=ISBN 81-297-0213-4


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