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Scalar Chain
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 **Lorentz scalar, a quantity in the theory of relativity which is invariant under a Lorentz transformation **Pseudoscalar, a quantity that behaves like a scalar, except that it changes sign under a parity inversion *Scalar (computing), any non-composite value *Scalar boson, in physics, a boson subatomic particle whose spin equals zero See also *dot product, also known as scalar product *dimensionless quantity, also known as scalar quantity *Inner product space *Scalar field *Scale (music) *Scaler (other) *''Pterophyllum scalare'' (Lichtenstein, 1823), a species of freshwater angelfish * Scala (other) Scala or SCALA may refer to: Automobiles * Renault Scala, multiple automobile models * Škoda Scala, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Scalar (mathematics)
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. Generally speaking, a vector space may be defined by using any field instead of real numbers (such as complex numbers). Then scalars of that vector space will be elements of the associated field (such as complex numbers). A scalar product operation – not to be confused with scalar multiplication – may be defined on a vector space, allowing two vectors to be multiplied in the defined way to produce a scalar. A vector space equipped with a scalar product is called an inner product space. A quantity described by multiple scalars, such as having both direction and magnitude, is called a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Scalar (physics)
Scalar quantities or simply scalars are physical quantities that can be described by a single pure number (a ''scalar'', typically a real number), accompanied by a unit of measurement, as in "10cm" (ten centimeters). Examples of scalar are length, mass, charge, volume, and time. Scalars may represent the magnitude of physical quantities, such as speed is to velocity. Scalars do not represent a direction. Scalars are unaffected by changes to a vector space basis (i.e., a coordinate rotation) but may be affected by translations (as in relative speed). A change of a vector space basis changes the description of a vector in terms of the basis used but does not change the vector itself, while a scalar has nothing to do with this change. In classical physics, like Newtonian mechanics, rotations and reflections preserve scalars, while in relativity, Lorentz transformations or space-time translations preserve scalars. The term "scalar" has origin in the multiplication o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Lorentz Scalar
In a relativistic theory of physics, a Lorentz scalar is a scalar expression whose value is invariant under any Lorentz transformation. A Lorentz scalar may be generated from, e.g., the scalar product of vectors, or by contracting tensors. While the components of the contracted quantities may change under Lorentz transformations, the Lorentz scalars remain unchanged. A simple Lorentz scalar in Minkowski spacetime is the ''spacetime distance'' ("length" of their difference) of two fixed events in spacetime. While the "position"-4-vectors of the events change between different inertial frames, their spacetime distance remains invariant under the corresponding Lorentz transformation. Other examples of Lorentz scalars are the "length" of 4-velocities (see below), or the Ricci curvature in a point in spacetime from general relativity, which is a contraction of the Riemann curvature tensor there. Simple scalars in special relativity Length of a position vector In special rel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Pseudoscalar
In linear algebra, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion while a true scalar does not. A pseudoscalar, when multiplied by an ordinary vector, becomes a '' pseudovector'' (or ''axial vector''); a similar construction creates the pseudotensor. A pseudoscalar also results from any scalar product between a pseudovector and an ordinary vector. The prototypical example of a pseudoscalar is the scalar triple product, which can be written as the scalar product between one of the vectors in the triple product and the cross product between the two other vectors, where the latter is a pseudovector. In physics In physics, a pseudoscalar denotes a physical quantity analogous to a scalar. Both are physical quantities which assume a single value which is invariant under proper rotations. However, under the parity transformation, pseudoscalars flip their signs while scalars do not. As reflections through a plane ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Scalar (computing)
Scalar processors are a class of computer processors that process only one data item at a time. Typical data items include integers and floating point numbers. Classification A scalar processor is classified as a single instruction, single data ( SISD) processor in Flynn's taxonomy. The Intel 486 is an example of a scalar processor. It is to be contrasted with a vector processor where a single instruction operates simultaneously on multiple data items (and thus is referred to as a single instruction, multiple data (SIMD) processor). The difference is analogous to the difference between scalar and vector arithmetic. The term ''scalar'' in computing dates to the 1970 and 1980s when vector processors were first introduced. It was originally used to distinguish the older designs from the new vector processors. Superscalar processor A superscalar processor (such as the Intel P5) may execute more than one instruction during a clock cycle by simultaneously dispatching multiple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Scalar Boson
A scalar boson is a boson whose spin equals zero. A ''boson'' is a particle whose wave function is symmetric under particle exchange and therefore follows Bose–Einstein statistics. The spin–statistics theorem implies that all bosons have an integer-valued spin. ''Scalar'' bosons are the subset of bosons with zero-valued spin. The name ''scalar boson'' arises from quantum field theory, which demands that fields of spin-zero particles transform like a scalar under Lorentz transformation (i.e. are Lorentz invariant). A pseudoscalar boson is a scalar boson that has odd parity, whereas "regular" scalar bosons have even parity. Examples Scalar * The only fundamental scalar boson in the Standard Model of particle physics is the Higgs boson, the existence of which was confirmed on 14 March 2013 at the Large Hadron Collider by CMS and ATLAS. As a result of this confirmation, the 2013 Nobel Prize in Physics was awarded to Peter Higgs and François Englert. * Various known ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dot Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a Scalar (mathematics), scalar as a result". It is also used for other symmetric bilinear forms, for example in a pseudo-Euclidean space. Not to be confused with scalar multiplication. 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 Euclidean vector, vectors is widely used. It is often called the inner product (or rarely the projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see ''Inner product space'' for more). It should not be confused with the cross product. Algebraically, the dot product is the sum of the Product (mathematics), products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
