Linked from

The 16 pages that link to Invariant subspace, each with the reason it gives.

• EigenvalueRelated: An eigenvector spans the simplest nonzero invariant subspace.

• Representation theoryRelated: Invariant subspaces reveal whether an action splits into smaller representations.

• Fixed pointCompared with: Invariance preserves a whole subspace, rather than leaving one point unchanged.

• Invariant (mathematics)Broader topic: Here the preserved object is a subspace under linear transformations.

• Group representationBroader topic: Such subspaces show when a representation contains smaller representations.

• Jordan normal formRelated: The spans of initial segments of Jordan chains form invariant subspaces.

• EigenvectorNarrower topic: An eigenvector spans the simplest possible invariant subspace.

• Irreducible representationRelated: A representation is irreducible precisely when its only invariant subspaces are zero and the whole space.

• Jordan decompositionRelated: The decomposition respects the operator's generalized eigenspace splitting.

• Maschke's theoremBroader topic: The theorem splits each invariant subspace off as a direct summand.

• Schur's lemmaRelated: Kernels and images of intertwining maps are invariant subspaces.

• Engel's theoremRelated: The common annihilated vector spans a one-dimensional invariant subspace.

• Jordan–Chevalley decompositionRelated: Primary subspaces let the decomposition be built one eigenvalue family at a time.

• Lie's theoremRelated: The span of a common eigenvector is invariant, enabling induction on dimension.

• Invariant subspace problemBroader topic: This is the structure whose existence the problem asks about.

• Rotations in 4-dimensional Euclidean spaceRelated: Every four-dimensional rotation decomposes into invariant planes on which it acts as a planar rotation.