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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 ...
Base quantity Symbol Description SI base unit Dimension Comments Amount of substance: n: 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: extensive: Time: t: The duration of ...
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.
In science, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. [1] [2] [3] An example of a scalar field is a weather map, with the surface temperature described by assigning a number to each point on the map.
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.
A physical quantity (or simply quantity) [1] [a] is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value , which is the algebraic multiplication of a numerical value and a unit of measurement .
Others [5] [6] define weight as a scalar quantity, the magnitude of the gravitational force. Yet others [ 7 ] define it as the magnitude of the reaction force exerted on a body by mechanisms that counteract the effects of gravity: the weight is the quantity that is measured by, for example, a spring scale.
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.