KnowraSpectral theoremLinked fromLinked fromThe 10 pages that link to Spectral theorem, each with the reason it gives.All 10Related 7Narrower topic 2Compared with 1Singular value decompositionNarrower topic: The decomposition extends spectral diagonalization to rectangular and nonnormal matrices.Characteristic polynomialRelated: Its eigenvalues, obtained as polynomial roots, determine the diagonal form.Invariant subspaceRelated: Its decompositions identify invariant subspaces associated with spectral values.Cayley–Hamilton theoremCompared with: Unlike the Cayley–Hamilton theorem, spectral results require conditions such as normality or self-adjointness.Symmetric matrixRelated: It gives the central structural decomposition of symmetric matrices.Diagonal matrixRelated: Real symmetric matrices can be represented diagonally in an orthonormal eigenbasis.Sylvester's law of inertiaRelated: It diagonalizes the matrix of a real quadratic form using an orthogonal change of variables.Kantorovich inequalityRelated: Expanding the vector in an eigenbasis reduces the bound to eigenvalue extremes.Cochran's theoremRelated: Diagonalization exposes the eigenvalues and projections that govern normal quadratic forms.Kosambi–Karhunen–Loève theoremNarrower topic: The covariance-operator decomposition is an instance of this broader operator principle.