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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 ...
A scalar field is a tensor field of order zero, [3] and the term "scalar field" may be used to distinguish a function of this kind with a more general tensor field, density, or differential form. The scalar field of ((+)) oscillating as increases. Red represents positive values, purple represents negative values, and sky blue represents ...
The final column lists some special properties that some of the quantities have, such as their scaling behavior (i.e. whether the quantity is intensive or extensive), their transformation properties (i.e. whether the quantity is a scalar, vector, matrix or tensor), and whether the quantity is conserved.
A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantified as m=n kg, where n is the numerical value and kg is the unit symbol (for kilogram). Quantities that are vectors have, besides numerical value ...
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
[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. A surface wind map, [4] assigning an arrow to each point on a map that describes the wind speed and direction at that point, is an example of a vector field, i.e. a 1-dimensional (rank-1) tensor field ...
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.
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.