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  • Extension of scalars — In abstract algebra, extension of scalars is a means of producing a module over a ring S from a module over another ring R, given a homomorphism f : R o S between them. Intuitively, the new module admits multiplication by more scalars than the… …   Wikipedia

  • Restriction of scalars — In abstract algebra, restriction of scalars is a procedure of creating a module over a ring R from a module over another ring S, given a homomorphism f : R o S between them. Intuitively speaking, the resulting module remembers less information… …   Wikipedia

  • Optical scalars — In general relativity, optical scalars are a set of scalars that describe various properties of null geodesic congruences. The three optical scalars used in general relativity are expansion, shear and twist (vorticity) and were first defined and… …   Wikipedia

  • rascals — scalars …   Anagrams dictionary

  • Trace (linear algebra) — In linear algebra, the trace of an n by n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii represents the entry on the ith row and ith column …   Wikipedia

  • Weil restriction — 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… …   Wikipedia

  • Field extension — In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For… …   Wikipedia

  • Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

  • Carminati-McLenaghan invariants — In general relativity, the Carminati McLenaghan invariants or CM scalars are a set of 16 scalar curvature invariants for the Riemann tensor. This set is usually supplemented with at least two additional invariants.Mathematical definitionThe CM… …   Wikipedia

  • Scalar (mathematics) — In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector.More generally, the scalars… …   Wikipedia

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