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2. Scalar (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Scalar_(mathematics)

   A scalar is an element of a field which is used to define a vector space.In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector.

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4. Conservative vector field - Wikipedia

   en.wikipedia.org/wiki/Conservative_vector_field

   The conservative vector fields correspond to the exact-forms, that is, to the forms which are the exterior derivative of a function (scalar field) on . The irrotational vector fields correspond to the closed 1 {\displaystyle 1} -forms , that is, to the 1 {\displaystyle 1} -forms ω {\displaystyle \omega } such that d ω = 0 {\displaystyle d ...

5. Vector (mathematics and physics) - Wikipedia

   en.wikipedia.org/wiki/Vector_(mathematics_and...

   The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces are kinds of vector spaces based on different kinds of scalars: real numbers and complex numbers. Scalars can also be, more generally, elements of any field.

6. Examples of vector spaces - Wikipedia

   en.wikipedia.org/wiki/Examples_of_vector_spaces

   Vector addition is just matrix addition and scalar multiplication is defined in the obvious way (by multiplying each entry by the same scalar). The zero vector is just the zero matrix. The dimension of F m×n is mn. One possible choice of basis is the matrices with a single entry equal to 1 and all other entries 0.

7. Complex vector bundle - Wikipedia

   en.wikipedia.org/wiki/Complex_vector_bundle

   If E is a complex vector bundle, then the conjugate bundle ¯ of E is obtained by having complex numbers acting through the complex conjugates of the numbers. Thus, the identity map of the underlying real vector bundles: ¯ = is conjugate-linear, and E and its conjugate E are isomorphic as real vector bundles.

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9. Ordered vector space - Wikipedia

   en.wikipedia.org/wiki/Ordered_vector_space

   A subset of a vector space is called a cone if for all real >,.A cone is called pointed if it contains the origin. A cone is convex if and only if +. The intersection of any non-empty family of cones (resp. convex cones) is again a cone (resp. convex cone); the same is true of the union of an increasing (under set inclusion) family of cones (resp. convex cones).