Definitions

1. A quadratic form is integral if its coefficients as a polynomial are integers.
2. This quadratic form is split into positive and negative parts, in contrast to the positive definite form on the algebra of quaternions.

Primitive Form

1. From the geometric equivalent problem, we can obtain a quadratic form, which becomes the primitive form of the secular equation.

Alternating Form

1. This is a quadratic form for n even, and an alternating form for n odd, because of the graded-commutative nature of the cohomology ring.

Dirichlet Form

1. One simple thing that deserves to be emphasized is that a Dirichlet form is not a kind of quadratic form on an abstract vector space.

Matrix

1. The goal in this line of research is to determine properties of a matrix, a linear system, or a quadratic form, that are forced by the signs (i.e.

Lorentz Transformations

1. Since the determinant of X is identified with the quadratic form Q, SL(2, C) acts by Lorentz transformations. (Web site)

Signature

1. The pair of integers (p, q) is called the signature of the quadratic form.
2. The quadratic form defining the Plücker relation comes from a symmetric bilinear form of signature (3,3).

Tangent Space

1. The inclusion defines a quadratic form on the tangent space to the surface at by restricting the canonical scalar product on.

Second Fundamental Form

1. In view of Proposition 1, it is customary to regard the second fundamental form as a quadratic form, as it done with the first fundamental form.

Case

1. In the case of a (pseudo -) Riemannian manifold, the tangent spaces come equipped with a natural quadratic form induced by the metric.
2. In the case of a (pseudo -) Riemannian manifold, the tangent space s come equipped with a natural quadratic form induced by the metric. (Web site)

Form

1. Also like the octonions, they form a composition algebra since the quadratic form N is multiplicative. (Web site)

Quaternions

1. Quaternions have received another boost from number theory because of their relation to quadratic form s. (Web site)

Conic Section

1. A modern view of the unification of the sphere and hyperboloid uses the idea of a conic section as a slice of a quadratic form. (Web site)

Scalar

1. The quadratic form on a scalar is just Q(λ) = λ2.

Scalar Product

1. The case where X is F, and we have a bilinear form, is particularly useful (see for example scalar product, inner product and quadratic form). (Web site)

Discriminant

1. The archetypal example of an invariant is the discriminant B 2 − 4 AC of a binary quadratic form Ax 2 + Bxy + Cy 2. (Web site)

Orthogonal Group

1. The first point is that quadratic form s over a field can be identified as a Galois H 1, or twisted forms (torsor s) of an orthogonal group.
2. As with the orthogonal group, the projective orthogonal group can be generalized in two main ways: changing the field or changing the quadratic form. (Web site)

Nondegenerate

1. In this section we assume that V is finite dimensional and the quadratic form Q is nondegenerate.

Metric Tensor

1. Signature of the quadratic form defined by a given metric tensor.

Vector Space

1. Let V be a vector space over a field K, and let Q: V → K be a quadratic form on V. In most cases of interest the field K is either R, C or a finite field.
2. Suppose that U has even dimension and a non-singular bilinear form with discriminant d, and suppose that V is another vector space with a quadratic form. (Web site)

Clifford Algebra

1. Given a vector space V and a quadratic form g an explicit matrix representation of the Clifford algebra C ℓ(V, g) can be defined as follows. (Web site)

Quadratic Form

1. Mathematical examples Some well-known examples of tensors in differential geometry are quadratic form s, such as metric tensor s, and the curvature tensor.
2. It can be also generalized to arbitrary codimension, in which case it is a quadratic form with values in the normal space.
3. In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. (Web site)

Categories

1. Clifford Algebra
2. Metric Tensor
3. Topological Spaces > Manifolds > Surfaces > Second Fundamental Form
4. Bilinear Form
5. Normal Space
6. Books about "Quadratic Form" in Amazon.com
   

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