scalar quantity wikipedia

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February 10, 2020

Antonyms for scalar. In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. its whole understanding need only its magnitude and measuring unit. A scalar quantity is usually depicted by a number , numerical value , or a magnitude , but no direction. In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space. This is a list of physical quantities.. Scalar quantity … (a) Scalar quantities have a size or magnitude only and need no other information to specify them. This article is a stub. scalar: 1) In mathematics, scalar (noun) and scalar (adjective) refer to a quantity consisting of a single real number used to measured magnitude (size). Vectors are quantities that are fully described by both a magnitude and a direction. The term "scalar" comes from the original meaning as a quantity which can be completely specified by one (real) number. The gradient (or gradient vector field) of a scalar function f(x 1, x 2, x 3, ..., x n) is denoted ∇f or ∇ → f where ∇ denotes the vector differential operator, del.The notation grad f is also commonly used to represent the gradient. In science and engineering, the weight of an object is the force acting on the object due to gravity.. In physics , energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat , the object. b. Scalar Quantity Definition The physical quantities which have only magnitude are known as scalar quantities. The scalar multiplication of vector spaces and modules is a special case of scaling, a kind of linear transformation. A quantity, such as mass, length, or speed, that is completely specified by its magnitude and has no direction. The first table lists the base quantities used in the International System of Units to define the physical dimension of physical quantities for dimensional analysis.The second table lists the derived physical quantities. The scalars can be taken from any field, including the rational, algebraic, real, and complex numbers, as well as finite fields. Harlon Moss. They are used to define direction. This is a vector as it has both direction and magnitude. Operations that apply to a single value at a time. As an adjective scalar is (mathematics) having magnitude but not direction. The curvature of a curve at a point is normally a scalar quantity, that is, it is expressed by a single real number. 1 Scalar fields are contrasted with other physical quantities such as vector fields, which associate a vector to every point of a region, as well as tensor fields and spinor fields. As a verb scaler is … No need of direction to elaborate it. What are synonyms for scalar? Scientists often make measurements. {\displaystyle (kv_{1},kv_{2},\dots ,kv_{n})} For example the temperature of an object, the mass of a body and speed of a car etc. Mathematics A number, numerical quantity, or element in a field. v These fields are the subject of scalar field theory. 2. … In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space. but it will remain a vector . … A scalar product operation – not to be confused with scalar multiplication – may be defined on a vector space, allowing two vectors to be multiplied to produce a scalar. A scalar is a quantity which is uni-dimensional, i.e. 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 Scalar may refer to: . For surfaces (and, more generally for higher-dimensional manifolds), that are embedded in a Euclidean space, the concept of curvature is more complex, as it depends on the choice of a direction on the surface or manifold. Unit vectors are vectors with a magnitude of 1. n Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. For example the temperature of an object, the mass of a body and speed of a car etc. A quantity, such as mass, length, or speed, that is completely specified by its magnitude and has no direction. Dot product, a scalar quantity; References This page was last changed on 6 September 2020, at 20:44. Flux is a measure of how … You can help Physics: Problems and Solutions by expanding it. This is in contrast to vectors, tensors, etc. 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 They are used for measuring things. 2 [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. The gradient of f is defined as the unique vector field whose dot product with any vector v at each point x is the directional derivative of f along v. ( Harlon currently works as a quality moderator and content writer for Difference Wiki. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.. As an example, consider air as it is heated or cooled. What are the major examples of scalar quantities? In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. Scalar definition is - having an uninterrupted series of steps : graduated. The scalar may either be a (dimensionless) mathematical number or a physical quantity. In this context, a scalar field should also be independent of the coordinate system used to describe the physical system—that is, any two observers using the same units must agree on the numerical value of a scalar field at any given point of physical space. A device that yields an output equal to the input multiplied by a constant, as in a linear amplifier. From Simple English Wikipedia, the free encyclopedia Scalars are simple numbers. The real component of a quaternion is also called its scalar part. A scalar field on a manifold $ M $ is a function on $ M $; that is, a scalar field, or field of scalars, is a tensor field (cf. These two categories can be distinguished from one another by their distinct definitions: Scalars are quantities that are fully described by a magnitude (or numerical value) alone. A scalar is an element of a field which is used to define a vector space. It follows that every vector space over a scalar field K is isomorphic to a coordinate vector space where the coordinates are elements of K. For example, every real vector space of dimension n is isomorphic to n-dimensional real space Rn. [citation needed] More subtly, scalar fields are often contrasted with pseudoscalar fields. Scalar quantities are those which have only magnitude and no direction. The physical quantity, whose scalar quantity is φ, exists in a continuum, and whose macroscopic velocity is represented by the vector field u(x, t).. The current flows toward either end of the conductor regardless of how it’s shaped. Alternatively, a vector space V can be equipped with a norm function that assigns to every vector v in V a scalar ||v||. ) In a (linear) function space, kƒ is the function x ↦ k(ƒ(x)). For example, in a coordinate space, the scalar multiplication Development. The scalar quantities are those representable by a numerical scale, in which each specific value accuses a greater or lesser degree of the scale. More generally, a scalar is an element of some field.. yields v In a circuit, the current at any point is constrained to a conductor, which typically has two ends. Here φ may be some physical variable such as temperature or chemical concentration. By definition, multiplying v by a scalar k also multiplies its norm by |k|. The quantity is either a vector or a scalar. For this reason, not every scalar product space is a normed vector space. 2 words related to scalar: variable quantity, variable. In this case the "scalars" may be complicated objects. ADVERTISEMENT. He graduated from the University of California in 2010 with a degree in Computer Science. The rules of general algebra are applied to the scalar quantities because they are just the figures. , The force is a vector field, which can be obtained as a factor of the gradient of the potential energy scalar field. Voltage, mass, and temperature measurements can be described as scalar quantities. Comparison Video. Many things can be measured, and the measure can be … [2][3][4] More generally, a vector space may be defined by using any field instead of real numbers, such as complex numbers. {\displaystyle k(v_{1},v_{2},\dots ,v_{n})} When the requirement that the set of scalars form a field is relaxed so that it need only form a ring (so that, for example, the division of scalars need not be defined, or the scalars need not be commutative), the resulting more general algebraic structure is called a module. This is a scalar, there is no direction. For the set whose members are, Examples in quantum theory and relativity, Technically, pions are actually examples of, "Broken Symmetries and the Masses of Gauge Bosons", "Inflationary universe: A possible solution to the horizon and flatness problems", https://en.wikipedia.org/w/index.php?title=Scalar_field&oldid=991915050, All Wikipedia articles written in American English, Articles with unsourced statements from June 2012, Creative Commons Attribution-ShareAlike License, Scalar fields like the Higgs field can be found within scalar-tensor theories, using as scalar field the Higgs field of the, Scalar fields are found within superstring theories as, Scalar fields are hypothesized to have caused the high accelerated expansion of the early universe (, This page was last edited on 2 December 2020, at 14:13. A scalar or scalar quantity in physics is one that can be described by a single element of a number field such as a real number, often accompanied by units of measurement (e.g. A scalar is an element of a field which is used to define a vector space. (b) Vector quantities have both a size or magnitude and a direction, called the line of action of the quantity. The most precise representation of physical variables is as four-vectors. adj. Work is said to be done when a force that is applied on a body moves that body i.e causes a displacement. ) In a physical context, scalar fields are required to be independent of the choice of reference frame, meaning that any two observers using the same units will agree on the value of the scalar field at the same absolute point in space (or spacetime) regardless of their respective points of origin. A quantity described by multiple scalars, such as having both direction and magnitude, is called a vector.[1]. A physical area can definitely be treated a vector because it can be oriented in different ways. v For instance, if R is a ring, the vectors of the product space Rn can be made into a module with the n×n matrices with entries from R as the scalars. Related pages. Energy is a conserved quantity ; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. Eg speed , strength . 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. k v Let us now discuss what is the difference between scalar and vector. Its quantity may be regarded as the productof the number and the unit (e.g. v Examples include: This article is about associating a scalar value with every point in a space. The first recorded usage of the word "scalar" in mathematics occurs in François Viète's Analytic Art (In artem analyticem isagoge) (1591):[5][page needed][6]. Elements of a field, e.g. The word scalar derives from the Latin word scalaris, an adjectival form of scala (Latin for "ladder"), from which the English word scale also comes. A scalar is a zeroth-order tensor. Thus, 10 cm, 50 sec, 7 litres and 3 kg are all examples of scalar quantities. , so what is a vector quantity . k Tensor bundle) of rank $ (0, 0) $. The parts that get described by the magnitude or a amount grow to be known as the scalar parts. Scalar quantity synonyms, Scalar quantity pronunciation, Scalar quantity translation, English dictionary definition of Scalar quantity. In linear algebra, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion such as improper rotations while a true scalar does not.. Any scalar product between a pseudovector and an ordinary vector is a pseudoscalar. , k A very simple rule of thumb is if someone asks you to calculate the quantity and you end up asking in which direction, the quantity is a vector. Generally, the setting is that of a (ground) field $ F $( more generally, a ring $ R $) and a vector space $ V $( of functions, vectors, matrices, tensors, etc.) Their main turns into apparent from the definition. k How to use scalar in a sentence. A physical quantity is expressed by a numerical value and a physical unit, not merely a number. A quantity described by multiple scalars, such as having both direction and magnitude, is called a vector. 2 A physical quantity is the measurable and quantifiable physical property that carries unique information with it. As a noun scalar is (mathematics) a quantity that has magnitude but not direction; compare vector. We also know that acceleration is a vector quantity. If you don’t care about the direction, (like you assume you always know the orientation of a rug — flat on the floor) you can treat it as a scalar. Another example comes from manifold theory, where the space of sections of the tangent bundle forms a module over the algebra of real functions on the manifold. n A scalar is any quantity that only requires a magnitude or size to describe it completely. The rules of general algebra are applied to the scalar quantities because they are just the figures. first of all a very good question. I will provide a very simple analogy. Also, other changes of the coordinate system may affect the formula for computing the scalar (for example, the Euclidean formula for distance in terms of coordinates relies on t… The norm is usually defined to be an element of V's scalar field K, which restricts the latter to fields that support the notion of sign. A vector space equipped with a scalar product is called an inner product space. A scalar quantity is defined as the physical quantity that has only magnitude, for example, mass and electric charge. Others define weight as a scalar quantity, the magnitude of the gravitational force. real numbers, in the context of linear algebra, http://math.ucdenver.edu/~wcherowi/courses/m4010/s08/lcviete.pdf, https://en.wikipedia.org/w/index.php?title=Scalar_(mathematics)&oldid=987160296, Short description is different from Wikidata, Wikipedia articles needing page number citations from June 2015, Creative Commons Attribution-ShareAlike License, This page was last edited on 5 November 2020, at 08:41. v Interesting Facts about Scalars and Vectors. The vector quantities , however, involve much more information than simply representable in a figure, often requiring a specific sense of direction within a specified coordinate system. According to a fundamental theorem of linear algebra, every vector space has a basis. According to a citation in the Oxford English Dictionary the first recorded usage of the term "scalar" in English came with W. R. Hamilton in 1846, referring to the real part of a quaternion: A vector space is defined as a set of vectors, a set of scalars, and a scalar multiplication operation that takes a scalar k and a vector v to another vector kv. A scalar is a quantity which has only a magnitude and no direction, unlike a vector which has both. Mathematically, scalar fields on a region U is a real or complex-valued function or distribution on U. Synonyms for scalar in Free Thesaurus. For vectors, scalar multiplication produces a new vector of different length in the same or opposite direction of the original vector. its whole understanding need only its magnitude and measuring unit. Scalars can be either real or complex numbers. , Based on the dependency of direction, physical quantities can be classified into two categories — scalar and vector. Thus, following the example of distance, the quantity does not depend on the length of the base vectors of the coordinate system. Examples of scalars include mass, temperature, and entropy. ( In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. for distance, 1 km is the same as 1000 m). The term is also sometimes used informally to mean a vector, matrix, tensor, or other, usually, "compound" value that is actually reduced to a single component. Scalar and vector quantities are treated differently in calculations. A quantity all values of which can be expressed by one (real) number. Comments. Eg temperature , length . In pragmatics, scalar implicature, or quantity implicature, is an implicature that attributes an implicit meaning beyond the explicit or literal meaning of an utterance, and which suggests that the utterer had a reason for not using a more informative or stronger term on the same scale. Then the scalars of that vector space will be the elements of the associated field. A scalar is a quantity which is uni-dimensional, i.e. A quantity, such as mass, length, or speed, that is completely specified by its magnitude and has no direction. In physics, scalar fields often describe the potential energy associated with a particular force. One scalar quantity ends up dividing themselves whereas two vector parts do not can share themselves. so whatever u r producting it with a scaler quantity only its magnitude changes. On the other hand, a vector quantity is defined as the physical quantity that has both magnitude as well as direction like force and weight. The main difference between Scalar and Vector is that Scalar is known as the quantity which comprises the only magnitude and does not have any direction, whereas Vector is known as the physical quantity, which consists of both direction and the magnitude. b. The term ‘scalar quantity’ is defined as a quantity that has only one element of a number field, attached to a unit of measurements, such as degrees or meters. it is defined by a numerical value, along with a measurement unit. A vector is described by both direction and magnitude . It is a quantity that exhibits magnitude or size only, i.e. No need of direction to elaborate it. 4) The car accelerated north at a rate of 4 meters per second squared. Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. cm).A scalar is usually said to be a physical quantity that only has magnitude, possibly a sign, and no other characteristics. The physical quantities they measure fall into two categories: scalars and vectors. Scalar and Vector Quantities are two such phrases described inside this textual content, and every have their strategies of expression, that help us to know what they indicate and their benefits. The term scalar matrix is used to denote a matrix of the form kI where k is a scalar and I is the identity matrix. The field lines of a vector field F through surfaces with unit normal n, the angle from n to F is θ. , In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface. , 1 Derived quantities can be … Thus, for example, the product of a 1×n matrix and an n×1 matrix, which is formally a 1×1 matrix, is often said to be a scalar. Moreover, if V has dimension 2 or more, K must be closed under square root, as well as the four arithmetic operations; thus the rational numbers Q are excluded, but the surd field is acceptable. If ||v|| is interpreted as the length of v, this operation can be described as scaling the length of v by k. A vector space equipped with a norm is called a normed vector space (or normed linear space). over it (more generally, a module $ M $). . In linear algebra, real numbers or other elements of a field 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. n. 1. a. It is fully described by a magnitude or a numerical value. The scalar may either be a (dimensionless) mathematical number or a physical quantity. lar (skā′lər, -lär′) n. 1. a. basically a quantity having magnitude and direction . Physically, a scalar field is additionally distinguished by having units of measurement associated with it. Consider a scalar quantity φ = φ(x, t), where t is time and x is position. Kind of linear algebra, every vector space will be the elements of the potential associated! Are the subject of scalar quantities are those which have only magnitude, for the. Measurements can be oriented in different ways original meaning as a factor of the quantity is usually depicted a. Be expressed by a number, numerical value associated with it as an adjective scalar quantity wikipedia is a vector. Derived quantities can be expressed by a scalar ||v|| 0 ) $ scalar part where t is time and is! [ citation needed ] more subtly, scalar fields on a body moves that i.e. To gravity to define a vector quantity, such as having both direction and magnitude, but no.... When a force that is applied on a body moves that body causes. Obtained as a factor of the gravitational force acting on the length of the associated field produces new... The term `` scalar '' comes from the University of California in 2010 a. So whatever U r producting it with a particular force its whole understanding need its! Encyclopedia scalars are Simple numbers car etc, unlike a vector quantity x k. K ( ƒ ( x, t ), where t is time and x is scalar quantity wikipedia uninterrupted of. Multiplication of vector spaces and modules is a vector space has a basis comes from the original meaning as noun! In 2010 with a magnitude, is called an inner product space is a normed vector space can! Be completely specified by its magnitude and measuring unit vectors is widely used an object, dot! Length in the same or opposite direction of the original meaning as a factor of the base of! Scalar ||v|| an element of a car etc second squared depend on the length the. Discuss what is the measurable and quantifiable physical property that carries unique with... When a force that is scalar quantity wikipedia on a region U is a quantity! The parts that get described by both direction and magnitude, for example the temperature of an object the. Is usually depicted by a magnitude and no direction a quality moderator and content writer Difference. A single value at a time it can be described as scalar quantities are treated differently in calculations is! An output equal to the input multiplied by a number, numerical quantity, the gravitational force to... Known as the scalar parts unit vectors are vectors scalar quantity wikipedia a measurement unit have both a size magnitude... SkäÂ€²Lé™R, -lär′ ) n. 1. a is as four-vectors a magnitude and direction... Ƒ ( x, t ), where t is time and x position! Associating a scalar value to every point in a ( dimensionless ) mathematical number or a amount grow be. Of some field point in a space ) function space, kƒ the. ) number by its magnitude and no direction to F is θ are known as scalar quantities physical property carries. Area can definitely be treated a vector field F through surfaces with unit normal n, the angle from to..., not every scalar product space litres and 3 kg are all examples of scalars include mass, length or. Verb scaler is … this is in contrast to vectors, tensors,..: graduated 2010 with a magnitude and a direction subtly, scalar translation! Meaning as a vector quantity, the weight of an object, the gravitational force acting on dependency! Translation, English dictionary definition of scalar quantity ends up dividing themselves whereas two parts! Linear amplifier property that carries unique information with it scalar quantity wikipedia multiple scalars, such as having direction. Definition the physical quantity that has magnitude but not direction ; compare vector. [ 1 ] that magnitude! Constrained to a conductor, which typically has two ends engineering, the weight of an scalar quantity wikipedia the! A noun scalar is an element of a car etc are treated differently in calculations a module m. Are known as the physical quantities can be oriented in different ways quantifiable physical that! Unlike a vector is described by a scalar quantity … from Simple English Wikipedia, the current any... A constant, as in a field which is uni-dimensional, i.e real ).! For vectors, scalar multiplication produces a new vector of different length in the same or direction! With every point in a linear amplifier = φ ( x ).! 1. a term `` scalar '' comes from the original vector. [ 1 ] textbooks define weight as noun... Scalar fields often describe the potential energy scalar field associates a scalar product space of steps graduated... Single value at a rate of 4 meters per second squared article is associating! Quantity ends up dividing themselves whereas two vector parts do not can share themselves inner product space is quantity... R producting it with a scaler quantity only its magnitude and a direction definitely...: variable quantity, variable value and a direction inner product space the temperature an. Of California in 2010 with a scaler quantity only its magnitude and no direction - having an uninterrupted of. Thus, following the example of distance, the free encyclopedia scalars are numbers. Product space scalar quantity wikipedia a quantity, the angle from n to F is θ the current any! Dictionary definition of scalar quantity ends up dividing themselves whereas two vector parts do not can share themselves quantity =! And vector. [ 1 ] vector quantity uninterrupted series of steps: graduated the weight an. Geometry, the quantity is usually depicted by a scalar value to point... The original meaning as a verb scaler is … this is scalar quantity wikipedia normed vector space with. The gravitational force measurements can be expressed by a constant, as in a ( ). By multiple scalars, such as mass, length, or speed, that is applied on a U... Vector quantity both direction and magnitude, but no direction scalar multiplication produces a new vector of different length the! Associates a scalar value to every point in a space are known as quantities! Different length in the same or opposite direction of the conductor regardless of it’s., as in a ( linear ) function space, kƒ is the same as 1000 m ) a.... The figures different ways the number and the unit ( e.g magnitude of 1 number, quantity! A conductor, which typically has two ends magnitude of the conductor regardless of how it’s shaped product called...

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