Linked from

The 17 pages that link to Jordan normal form, each with the reason it gives.

• EigenvalueRelated: It shows how repeated eigenvalues can coexist with too few independent eigenvectors.

• Matrix exponentialRelated: Jordan blocks make the exponential computable even when a matrix is not diagonalizable.

• Invariant subspaceRelated: Chains of invariant subspaces underlie the block decomposition.

• EigenvectorRelated: It describes transformations whose eigenvectors alone do not form a basis.

• Square matrixBroader topic: It describes square matrices that cannot be diagonalized.

• Camille JordanBroader topic: This celebrated algebraic result is named for Jordan, though his work ranged far beyond matrices.

• Spectral theoremCompared with: It handles matrices that lack a full eigenbasis, unlike the diagonalizable cases of the theorem.

• Cayley–Hamilton theoremCompared with: Jordan form offers another way to verify the theorem, but requires more structure than its general statement.

• Diagonal matrixCompared with: It replaces diagonal form when a matrix lacks enough independent eigenvectors.

• Spectral radiusRelated: Its blocks show how eigenvalue moduli and polynomial factors shape matrix-power growth.

• Jordan decompositionRelated: Its blocks reveal the semisimple and nilpotent contributions directly.

• Sylvester's law of inertiaCompared with: It classifies matrices under similarity rather than quadratic forms under congruence.

• Fundamental theorem of linear algebraCompared with: It analyzes eigenstructure, whereas the fundamental theorem concerns four subspaces for any matrix.

• Triangular matrixRelated: Jordan form is a specialized triangular structure that records eigenvalue multiplicities and generalized eigenvectors.

• Eigenvalues and eigenvectorsCompared with: It describes matrices that lack enough eigenvectors for diagonalization.

• Jordan–Chevalley decompositionRelated: Each block displays its eigenvalue and nilpotent contribution directly.

• Fitting lemmaRelated: The lemma separates the zero-eigenvalue part from the invertible part of a linear operator.