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The 17 pages that link to Minimal polynomial, each with the reason it gives.

• Algebraic numberRelated: It gives each algebraic number a canonical equation and determines its degree.

• Field extensionRelated: Its degree measures the extension generated by that element.

• Galois groupRelated: Automorphisms fixing the base field must send an element to another root of its minimal polynomial.

• Transcendental numberRelated: For an algebraic number, its minimal polynomial supplies a canonical equation witnessing algebraicity.

• Cyclotomic polynomialRelated: Φₙ is the minimal polynomial of every primitive nth root over the rational numbers.

• Jordan normal formRelated: Its root multiplicities give the largest block size for each eigenvalue.

• Splitting fieldRelated: Its roots determine the conjugates that must appear alongside an adjoined root.

• Cayley–Hamilton theoremRelated: It divides the characteristic polynomial and captures the matrix’s essential polynomial relations.

• Constructible numberRelated: Its degree over the rationals must be a power of two for a constructible number.

• Algebraic integerRelated: Its coefficients show whether an algebraic number is an algebraic integer.

• Algebraic number fieldRelated: It determines the degree and algebraic relations of a field generator.

• Jordan decompositionRelated: Its factorization into powers of distinct irreducibles governs the two parts.

• Normal extensionRelated: Its roots determine whether the element's conjugates all lie in the extension.

• Transcendence theoryRelated: Its existence for algebraic numbers contrasts with transcendence.

• Gelfond–Schneider theoremRelated: It encodes the algebraic nature of the base and exponent.

• Primitive element theoremRelated: A primitive element encodes the extension through its minimal polynomial.

• Jordan–Chevalley decompositionRelated: Its factorization into powers of distinct linear factors determines the decomposition’s components.