quadratic form

He also investigated, and wrote a book on, the theory of quadratic forms.

A given quadratic form may support several different types of spinors.

Let A be the matrix of the quadratic form q in a given basis.

The energy density is written if in quadratic form.

An indefinite quadratic form is one that takes on both positive and negative values.

The trace also plays a central role in the distribution of quadratic forms.

These are frequently studied in relation to the theory of quadratic forms.

His main publications were on quadratic forms and algebraic groups.

Lagrange gave a proof in 1775 that was based on his study of quadratic forms.

This example is called the hyperbolic plane in the theory of quadratic forms.

A homogeneous polynomial of degree 2 is a quadratic form.

The first of these is the class number formulae for binary quadratic forms.

This is further generalised to quadratic forms in linear spaces.

Remark: If we choose the field of complex numbers, there is no suitable quadratic form at all.

Every quadratic form in 5 or more variables over k is isotropic.

Quadratic forms can be expressed as where is a symmetric matrix.

Quadratic forms with the same core form are said to be similar or Witt equivalent.

A quadratic form representing all positive integers is sometimes called universal.

For example, in a pseudo-Euclidean space one has the use of a quadratic form:

For instance, it is possible to replace Euclidean distance by the value of a quadratic form.

Quaternions have received another boost from number theory because of their relationships with the quadratic forms.

Additionally let be a quadratic form on vector space .

It is known that the first quadratic form reflects the distance between two surface points and .

Historically, however, they arose in the study of quadratic forms and differential equations.

The inertia tensor in mechanics is an example of a quadratic form.