Homogenous polynomial

Quadratic form

A quadratic form over a field is a map from a finite vector space such that

for all and the corresponding polar form is a bilinear form. linalg A vector space equipped with a quadratic form is a Quadratic space. Equivalently, is an algebraic form of degree 2

or using a matrix

A space equipped with a quadratic form is called a quadratic space.

Further terminology

• See Further terminology

Properties

• Correspondence between quadratic forms and symmetric bilinear forms away from 2
• Correspondence between quadratic forms and alternating bilinear forms at 2
• Diagonalization of a quadratic form away from 2

Related

• Projective quadric

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