Quadratic form

In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example, the distance between two points in three-dimensional Euclidean space is found by taking the square root of a quadratic form involving six variables, the three coordinates of each of the two points.

Related Topics:
Mathematics - Homogeneous polynomial - Degree - Distance - Euclidean space

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Quadratic forms in one, two, and three variables are given by:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:F(x) = ax^2

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:F(x,y) = ax^2 + by^2 + cxy

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:F(x,y,z) = ax^2 + by^2 + cz^2 + dxy + exz + fyz

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Note that general quadratic functions and quadratic equations are not examples of quadratic forms.

Related Topics:
Quadratic function - Quadratic equation

~ ~ ~ ~ ~ ~ ~ ~ ~ ~