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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.
Download as PDF; Printable version; ... (mathematics) (1 C, 20 P) P. Scalar physical quantities (11 C, 13 P) Pages in category "Scalars" The following 8 pages are in ...
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]).
In mathematics, a linear form (also known as a linear functional, [1] a one-form, or a covector) is a linear map [nb 1] from a vector space to its field of scalars (often, the real numbers or the complex numbers).
In mathematics, restriction of scalars (also known as "Weil restriction") is a functor which, for any finite extension of fields L/k and any algebraic variety X over L, produces another variety Res L/k X, defined over k. It is useful for reducing questions about varieties over large fields to questions about more complicated varieties over ...
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