Linked from

The 29 pages that link to Field (mathematics), each with the reason it gives.

• Vector spaceRelated: Scalars come from a field, whose operations make scalar multiplication coherent.

• Quadratic formRelated: The underlying field affects diagonalization and whether a symmetric matrix represents the form.

• Évariste GaloisRelated: Fields provide the number systems in which polynomial roots and their symmetries are studied.

• Dual spaceRelated: The scalar field supplies the values taken by every functional in the dual.

• Scalar multiplicationRelated: Scalars come from a field, such as the real or complex numbers.

• Algebraic curveRelated: The coefficient field affects which points and geometric features a curve possesses.

• Rational pointRelated: The chosen field determines which coordinates count as rational.

• Leopold KroneckerRelated: Fields provide the setting for algebraic numbers and Kronecker’s results on equations.

• Local ringRelated: Quotients by maximal ideals are fields, including the residue field of a local ring.

• Polynomial remainder theoremRelated: Fields provide the familiar setting for polynomial division and the theorem.

• Algebra over a fieldRelated: Its elements provide the scalars used to define the algebra.

• Tits alternativeRelated: Linear groups are formed from matrices over a field.

• Steinitz exchange lemmaRelated: Vector-space scalars come from a field, which permits solving for a nonzero coefficient.