non-degenerate quadratic form

Let k be a field of characteristic not 2. Then a quadratic formMathworldPlanetmath Q over a vector spaceMathworldPlanetmath V (over a field k) is said to be , if its associated bilinear formPlanetmathPlanetmath:


is non-degenerate.

If we fix a basis 𝒃 for V, then Q(x) can be written as


for some symmetric matrixMathworldPlanetmath A over k. Then it’s not hard to see that Q is non-degenerate iff A is non-singular. Because of this, a non-degenerate quadratic form is also known as a non-singular quadratic form. A third name for a non-degenerate quadratic form is that of a regular quadratic form.

Title non-degenerate quadratic form
Canonical name NondegenerateQuadraticForm
Date of creation 2013-03-22 15:05:58
Last modified on 2013-03-22 15:05:58
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 6
Author CWoo (3771)
Entry type Definition
Classification msc 15A63
Classification msc 11E39
Classification msc 47A07
Synonym non degenerate quadratic form
Synonym non singular quadratic form
Defines non-degenerate quadratic form
Defines non-singular quadratic form
Defines regular quadratic form