Search results
Results from the WOW.Com Content Network
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.
A scalar in physics and other areas of science is also a scalar in mathematics, as an element of a mathematical field used to define a vector space.For example, the magnitude (or length) of an electric field vector is calculated as the square root of its absolute square (the inner product of the electric field with itself); so, the inner product's result is an element of the mathematical field ...
Mathematically, a scalar field on a region U is a real or complex-valued function or distribution on U. [1] [2] The region U may be a set in some Euclidean space, Minkowski space, or more generally a subset of a manifold, and it is typical in mathematics to impose further conditions on the field, such that it be continuous or often continuously differentiable to some order.
Scalar multiplication of a vector by a factor of 3 stretches the vector out. The scalar multiplications −a and 2a of a vector a. In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra [1] [2] [3] (or more generally, a module in abstract algebra [4] [5]).
Scalar may refer to: Scalar (mathematics) , an element of a field, which is used to define a vector space, usually the field of real numbers Scalar (physics) , a physical quantity that can be described by a single element of a number field such as a real number
For a scalar field theory with D spacetime dimensions, the only dimensionless parameter g n satisfies n = 2D ⁄ (D − 2). For example, in D = 4, only g 4 is classically dimensionless, and so the only classically scale-invariant scalar field theory in D = 4 is the massless φ 4 theory .
The search engine that helps you find exactly what you're looking for. Find the most relevant information, video, images, and answers from all across the Web.
In Cartesian coordinates, the divergence of a continuously differentiable vector field = + + is the scalar-valued function: = = (, , ) (, , ) = + +.. As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge.