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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 ...
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 ...
Dot product. In mathematics, the dot product or scalar product[ note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors ), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or ...
In mathematics and physics, a scalar field is a function associating a single number to every point in a space – possibly physical space. The scalar may either be a pure mathematical number ( dimensionless) or a scalar physical quantity (with units ). In a physical context, scalar fields are required to be independent of the choice of ...
The quantity proportional to the number of particles in a sample, with the Avogadro constant as the proportionality constant. mole (mol) N. extensive, scalar. Length. l. The one-dimensional extent of an object. metre (m) L.
Scalar (physics), a physical quantity that can be described by a single element of a number field such as a real number. Lorentz scalar, a quantity in the theory of relativity which is invariant under a Lorentz transformation. Pseudoscalar, a quantity that behaves like a scalar, except that it changes sign under a parity inversion.
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] ). In common geometrical contexts, scalar multiplication of a real Euclidean vector by a positive real number multiplies the magnitude of the vector without ...
Then, the scalar product of velocity with acceleration in Newton's second law takes the form = ˙ = = (), where the kinetic energy of the particle is defined by the scalar quantity, = = ˙ ˙. The result is the work–energy principle for particle dynamics, W = Δ K . {\displaystyle W=\Delta K.}