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The 25 pages that link to Quadratic form, each with the reason it gives.

• Cauchy–Schwarz inequalityRelated: The proof studies the nonnegative quadratic ‖x−ty‖² as t varies.

• Metric tensorRelated: Evaluating the metric twice on a vector gives its squared length.

• Hessian matrixRelated: The Hessian defines the quadratic curvature term in a local expansion.

• Equipartition theoremRelated: The theorem assigns its standard contribution to independent quadratic energy terms.

• Bilinear formRelated: A symmetric bilinear form determines a quadratic form through its diagonal values.

• Symmetric matrixRelated: The symmetric part of a matrix alone determines its quadratic form.

• Geometric algebraRelated: Its values set the metric relations built into a Clifford algebra.

• Conjugate gradient methodRelated: The system solution is the minimizer of a quadratic energy whose curvature is set by the matrix.

• James Joseph SylvesterRelated: Sylvester classified quadratic forms using their numbers of positive and negative terms.

• Helmut HasseRelated: Hasse studied when quadratic forms represent numbers over global and local fields.

• Hensel's lemmaRelated: Local solvability of quadratic forms often relies on lifting modular solutions.

• Sylvester's criterionRelated: Positive definiteness is defined through this expression, while the criterion tests its matrix.

• Fermat polygonal number theoremRelated: Polygonal-number representations become quadratic-form equations after multiplying by a fixed denominator.

• Titu's lemmaRelated: The lemma controls sums of squared terms, the basic structure of quadratic expressions.

• Bruck–Ryser–Chowla theoremRelated: Quadratic-form solvability provides the arithmetic framework behind the theorem’s restrictions.

• Degen's eight-square identityRelated: The sum of eight coordinate squares is the quadratic form whose multiplicativity is expressed.