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Two-form

 

 
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Two-form
 
 
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In linear algebra
Linear algebra

Linear algebra is the branch of mathematics concerned with the study of Euclidean vectors, vector spaces , linear maps , and system of linear equations....
, a two-form is another term for a bilinear form
Bilinear form

In mathematics, a bilinear form on a vector space V is a bilinear mapping V ? V ? F, where F is the field of scalars....
, typically used in informal discussions, or sometimes to indicate that the bilinear form is skew-symmetric.

In differential geometry, a two-form refers to a differential form
Differential form

In the mathematics fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates....
 of degree two. In other words, a two-form is an order (or "rank") 2 skew-symmetric covariant tensor field
Tensor field

In mathematics, physics and engineering, a tensor field is a very general concept of variable geometric quantity. It is used in differential geometry and the theory of manifolds, in algebraic geometry, in general relativity, in the analysis of stress and strain tensor in materials, and in numerous applications in the physical sciences and en...
.

For a given vector space, the space of two-forms is spanned by the wedge product of basis one-forms. See differential form
Differential form

In the mathematics fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates....









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In linear algebra
Linear algebra

Linear algebra is the branch of mathematics concerned with the study of Euclidean vectors, vector spaces , linear maps , and system of linear equations....
, a two-form is another term for a bilinear form
Bilinear form

In mathematics, a bilinear form on a vector space V is a bilinear mapping V ? V ? F, where F is the field of scalars....
, typically used in informal discussions, or sometimes to indicate that the bilinear form is skew-symmetric.

In differential geometry, a two-form refers to a differential form
Differential form

In the mathematics fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates....
 of degree two. In other words, a two-form is an order (or "rank") 2 skew-symmetric covariant tensor field
Tensor field

In mathematics, physics and engineering, a tensor field is a very general concept of variable geometric quantity. It is used in differential geometry and the theory of manifolds, in algebraic geometry, in general relativity, in the analysis of stress and strain tensor in materials, and in numerous applications in the physical sciences and en...
.

For a given vector space, the space of two-forms is spanned by the wedge product of basis one-forms. See differential form
Differential form

In the mathematics fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates....


See also

  • Mixed tensor
    Mixed tensor

    In tensor analysis, a mixed tensor is a tensor which is neither covariant nor contravariant. At least one of the indices of a mixed tensor will be a subscript and at least one of the indices will be a superscript ....
  • Metric tensor
    Metric tensor

    In the mathematics field of differential geometry, a metric tensor is a type of function defined on a manifold which takes as input a pair of tangent vectors v and w and produces a real number g in a way that generalizes many of the familiar properties of the dot product of Vector in Euclidean space....