Definition, Meaning & Anagrams | English word SCALARS

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Definitions of SCALARS

1. plural of scalar.

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Examples of Using SCALARS in a Sentence

• There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product.
• In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars.
• Again, since both quadratic forms are scalars and hence their product is a scalar, the expectation of their product is also a scalar.
• Array programming (also termed vector or multidimensional) languages generalize operations on scalars to apply transparently to vectors, matrices, and higher-dimensional arrays.
• In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars (often, the real numbers or the complex numbers).
• The fermions are in representations of , the gauge fields are in a representation of , and the scalars are in a representation of both (Gravitons are singlets with respect to both).
• The observed Lorentz invariance of space-time allows only the formation of condensates which are Lorentz scalars and have vanishing charge.
• Custom data types are allowed, but YAML natively encodes scalars (such as strings, integers, and floats), lists, and associative arrays (also known as maps, dictionaries or hashes).
• Given a polynomial expression, one can compute the expanded form of the represented polynomial by expanding with the distributive law all the products that have a sum among their factors, and then using commutativity (except for the product of two scalars), and associativity for transforming the terms of the resulting sum into products of a scalar and a monomial; then one gets the canonical form by regrouping the like terms.
• According to the representation theory of the Lorentz group, these quantities are built out of scalars, four-vectors, four-tensors, and spinors.
• Many mathematical dualities between objects of two types correspond to pairings, bilinear functions from an object of one type and another object of the second type to some family of scalars.
• This problem was discovered in field theories of interacting scalars and spinors, including quantum electrodynamics (QED), and Lehmann positivity led many to suspect that it is unavoidable.
• Trivially, all scalars and vectors (tensors of order 0 and 1) are totally antisymmetric (as well as being totally symmetric).
• Curvilinear coordinates are often used to define the location or distribution of physical quantities which may be, for example, scalars, vectors, or tensors.
• More generally, complexification is an example of extension of scalars – here extending scalars from the real numbers to the complex numbers – which can be done for any field extension, or indeed for any morphism of rings.
• In two and three dimensions the even subalgebra contains only scalars and bivectors, and each is of particular interest.
• Modern programming languages that support array programming (also known as vector or multidimensional languages) have been engineered specifically to generalize operations on scalars to apply transparently to vectors, matrices, and higher-dimensional arrays.
• An alternative way to write the above classification of scalars, pseudoscalars, vectors and pseudovectors is in terms of the representation space that each object transforms in.
• This "algebraization" of a manifold (replacing a geometric object with an algebra) leads to the notion of a C*-algebra – a commutative C*-algebra being precisely the ring of scalars of a manifold, by Banach–Stone, and allows one to consider noncommutative C*-algebras as non-commutative generalizations of manifolds.
• a subcategory having subobjects and direct sums, such that the C*-algebra of endomorphisms of the monoidal unit contains only scalars.
• In the presence of a volume form (such as given an inner product and an orientation), pseudovectors and pseudoscalars can be identified with vectors and scalars, which is routine in vector calculus, but without a volume form this cannot be done without making an arbitrary choice.
• Every quaternion algebra becomes a matrix algebra by extending scalars (equivalently, tensoring with a field extension), i.
• As a consequence, several physical quantities that are scalars in "classical" (non-relativistic) physics need to be combined with other quantities and treated as four-vectors or tensors.
• The decomposition states that the evolution equations for the most general linearized perturbations of the Friedmann–Lemaître–Robertson–Walker metric can be decomposed into four scalars, two divergence-free spatial vector fields (that is, with a spatial index running from 1 to 3), and a traceless, symmetric spatial tensor field with vanishing doubly and singly longitudinal components.
• The dyadic product is also associative with the dot and cross products with other vectors, which allows the dot, cross, and dyadic products to be combined to obtain other scalars, vectors, or dyadics.

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