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- Semi-simple_operator abstract "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. This is because such an operator always has an eigenvector; if it is, in addition, semi-simple, then it has a complementary invariant hyperplane, which itself has an eigenvector, and thus by induction is diagonalizable. Conversely, diagonalizable operators are easily seen to be semi-simple, as invariant subspaces are direct sums of eigenspaces, and any basis for this space can be extended to an eigenbasis.".
- Semi-simple_operator wikiPageID "7252030".
- Semi-simple_operator wikiPageRevisionID "544555496".
- Semi-simple_operator hasPhotoCollection Semi-simple_operator.
- Semi-simple_operator subject Category:Invariant_subspaces.
- Semi-simple_operator subject Category:Linear_algebra.
- Semi-simple_operator type Abstraction100002137.
- Semi-simple_operator type Attribute100024264.
- Semi-simple_operator type InvariantSubspaces.
- Semi-simple_operator type MathematicalSpace108001685.
- Semi-simple_operator type Set107999699.
- Semi-simple_operator type Space100028651.
- Semi-simple_operator type Subspace108004342.
- Semi-simple_operator comment "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.".
- Semi-simple_operator label "Matrice semi-simple".
- Semi-simple_operator label "Semi-simple operator".
- Semi-simple_operator sameAs Matrice_semi-simple.
- Semi-simple_operator sameAs m.025x9cj.
- Semi-simple_operator sameAs Q3299281.
- Semi-simple_operator sameAs Q3299281.
- Semi-simple_operator sameAs Semi-simple_operator.
- Semi-simple_operator wasDerivedFrom Semi-simple_operator?oldid=544555496.
- Semi-simple_operator isPrimaryTopicOf Semi-simple_operator.