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The 22 pages that link to Characteristic polynomial, each with the reason it gives.

• EigenvalueRelated: Its roots locate the scalars satisfying the eigenvalue equation.

• DeterminantRelated: Determinants encode eigenvalues through the characteristic polynomial.

• CoefficientRelated: Its coefficients summarize matrix properties such as trace and determinant.

• Jordan normal formRelated: Its roots identify the eigenvalues represented in the Jordan blocks.

• Minimal polynomialCompared with: It shares roots and divisibility relations with the minimal polynomial but can have larger degree.

• Polynomial rootRelated: Its roots are the matrix’s eigenvalues, linking polynomial root-finding to linear algebra.

• EigenvectorRelated: Its roots identify the scale factors needed to find eigenvectors.

• Square matrixRelated: Its coefficients and roots summarize key properties of the matrix.

• Eigenvalue problemRelated: Its roots give the eigenvalues of a finite-dimensional matrix.

• Cayley–Hamilton theoremBroader topic: The theorem’s central ingredient is the polynomial that the matrix must satisfy.

• Lucas sequenceRelated: Its roots produce closed forms for sequences obeying the Fibonacci recurrence.

• Principal symbolCompared with: For systems, taking a determinant of the principal symbol produces a related polynomial, not the symbol itself.

• Spectral radiusRelated: Its roots provide the values whose largest modulus defines the spectral radius.

• Routh–Hurwitz stability criterionRelated: For linear systems, this is the polynomial to which the criterion is applied.

• Laplace expansionRelated: Cofactor expansion can derive this polynomial, especially for small matrices.

• Newton's identitiesRelated: Its coefficients and eigenvalue power sums are linked by these formulas.

• Spectral graph theoryRelated: It packages a graph matrix’s spectrum into an algebraic invariant.

• Eigenvalues and eigenvectorsRelated: Its roots identify the scaling factors that allow nonzero vectors to retain their directions.

• Jordan–Chevalley decompositionRelated: Its roots identify the eigenvalues that organize the semisimple part.

• Matching polynomialCompared with: For forests it coincides with the matching polynomial, but cycles generally separate them.

• Gershgorin circle theoremRelated: The theorem encloses the roots of this polynomial without solving for them.

• Leibniz formula for determinantsRelated: Its determinant can be expanded by the same signed permutation sum.