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The 69 pages that link to Eigenvalue, each with the reason it gives.

• Sylvester's law of inertiaRelated: The signs of the eigenvalues give the positive and negative counts in an orthogonal diagonalization.

• Crystallographic restriction theoremRelated: Rotation eigenvalues encode the angle whose allowed orders the theorem limits.

• Euler's rotation theoremRelated: Every three-dimensional proper rotation has eigenvalue one, yielding an unchanged axis direction.

• QuantizationRelated: Possible outcomes of measuring an observable are its operator’s eigenvalues.

• Sylvester's criterionRelated: A Hermitian matrix is positive definite exactly when all its eigenvalues are positive.

• Triangular matrixRelated: The eigenvalues of a triangular matrix are its diagonal entries, counted with multiplicity.

• Jordan–Chevalley decompositionRelated: The semisimple component preserves the operator’s eigenvalues.

• Perron–Frobenius theoremNarrower topic: The theorem singles out one eigenvalue with maximal absolute value.

• Selberg trace formulaRelated: Laplacian eigenvalues form the discrete spectral data on the formula’s left side.

• Gershgorin circle theoremNarrower topic: The theorem locates these values by comparing a largest eigenvector coordinate with its matrix row.

• Kantorovich inequalityBroader topic: Only the smallest and largest eigenvalues determine the sharp constant.

• Sign (mathematics)Related: An eigenvalue's sign can indicate whether its eigendirection is preserved or reversed.

• Anna Johnson Pell WheelerRelated: Eigenvalues organize the spectral analysis of operators studied in Wheeler's work.

• Hartman–Grobman theoremRelated: The eigenvalues of the Jacobian determine whether the fixed point is hyperbolic.

• Hellmann–Feynman theoremRelated: The theorem tracks how an energy eigenvalue changes as the Hamiltonian varies.

• Ioana DumitriuBroader topic: Eigenvalues are central objects in her matrix and network research.

• Rotations in 4-dimensional Euclidean spaceRelated: Complex eigenvalues of real rotations encode their planar rotation angles.

• Spin-½Related: Measuring spin along an axis yields eigenvalues plus or minus one-half times the reduced Planck constant.

• Value (mathematics)Broader topic: Eigenvalues are particular quantities characterized by a transformation's action.