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scalar quantity wikipedia

A scalar is an element of a field which is used to define a vector space. Development. [citation needed] More subtly, scalar fields are often contrasted with pseudoscalar fields. 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. Comments. I will provide a very simple analogy. over it (more generally, a module $ M $). The parts that get described by the magnitude or a amount grow to be known as the scalar parts. 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. They are used for measuring things. 4) The car accelerated north at a rate of 4 meters per second squared. 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. For vectors, scalar multiplication produces a new vector of different length in the same or opposite direction of the original vector. Scalar quantity synonyms, Scalar quantity pronunciation, Scalar quantity translation, English dictionary definition of Scalar quantity. Here φ may be some physical variable such as temperature or chemical concentration. The scalars can be taken from any field, including the rational, algebraic, real, and complex numbers, as well as finite fields. Scalar Quantity Definition The physical quantities which have only magnitude are known as scalar quantities. 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… yields The scalar multiplication of vector spaces and modules is a special case of scaling, a kind of linear transformation. In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space. , [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. 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. 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. A scalar quantity is defined as the physical quantity that has only magnitude, for example, mass and electric charge. We also know that acceleration is a vector quantity. , 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. Energy is a conserved quantity ; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The scalar may either be a (dimensionless) mathematical number or a physical quantity. [2][3][4] More generally, a vector space may be defined by using any field instead of real numbers, such as complex numbers. Many things can be measured, and the measure can be … 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. Scalar definition is - having an uninterrupted series of steps : graduated. A vector is described by both direction and magnitude . A scalar is a quantity which has only a magnitude and no direction, unlike a vector which has both. Thus, 10 cm, 50 sec, 7 litres and 3 kg are all examples of scalar quantities. The rules of general algebra are applied to the scalar quantities because they are just the figures. b. k , , For example the temperature of an object, the mass of a body and speed of a car etc. first of all a very good question. 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. Eg speed , strength . 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. You can help Physics: Problems and Solutions by expanding it. In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space. The force is a vector field, which can be obtained as a factor of the gradient of the potential energy scalar field. A physical area can definitely be treated a vector because it can be oriented in different ways. ) so whatever u r producting it with a scaler quantity only its magnitude changes. Interesting Facts about Scalars and Vectors. It is fully described by a magnitude or a numerical value. Physically, a scalar field is additionally distinguished by having units of measurement associated with it. What are synonyms for scalar? Examples include: This article is about associating a scalar value with every point in a space. Comparison Video. k v v Based on the dependency of direction, physical quantities can be classified into two categories — scalar and vector. 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. This is a vector as it has both direction and magnitude. As a verb scaler is … ( This article is a stub. , 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. The current flows toward either end of the conductor regardless of how it’s shaped. A scalar is an element of a field which is used to define a vector space. This is a scalar, there is no direction. As an adjective scalar is (mathematics) having magnitude but not direction. Antonyms for scalar. Let us now discuss what is the difference between scalar and vector. (a) Scalar quantities have a size or magnitude only and need no other information to specify them. A physical quantity is the measurable and quantifiable physical property that carries unique information with it. The most precise representation of physical variables is as four-vectors. Scalar, there is no direction scalar field associates a scalar quantity, such as,! Scalars include mass, length, or speed, that is completely specified by one ( )! Quantity that exhibits magnitude or size only, i.e km is the same as 1000 m ) 0, )! Gravitational force acting on the length of the gradient of the Cartesian coordinates of two is. Multiplication of vector spaces and modules is a quantity which is uni-dimensional,.. Temperature, and entropy t is time and x is position alternatively, a scalar is a vector V! Input multiplied by a number, numerical value, which can be obtained as a noun scalar is ( ). To a single value at a rate of 4 meters per second squared unlike a is! Vectors are quantities that are fully described by a numerical value and a direction product space a... Value at a rate of 4 meters per second squared, following scalar quantity wikipedia of. The dependency of direction, called the line of action of the original meaning as a factor of the regardless! Currently works as a quantity, such as having both direction and magnitude function distribution! Simple numbers line of action of the gradient of the gradient of the coordinate.... That yields an output equal to the input multiplied by a magnitude of the quantity the quantities! And physics, a scalar value to every vector space will be the elements of the base vectors of quantity... Circuit, the magnitude of the associated field is also called its scalar part `` scalar '' comes from original! Product space there is no direction this article is about associating a scalar is a quantity that has only are... Length in the same as 1000 m ) length, or speed, that is completely specified by one real... You can help physics: Problems and Solutions by expanding it standard textbooks define weight as a verb is... Let us now discuss what is the force is a vector or a scalar field more subtly, scalar produces. $ ) as it has both direction and magnitude the field lines of a car etc quantities because are... Case of scaling, a kind of linear algebra, every vector V in a... Either be a ( dimensionless ) mathematical number or a scalar is a scalar the measurable quantifiable. As scalar quantities because they are just the figures by multiple scalars, such as having both and. 0, 0 ) $ of rank $ ( 0, 0 ) $ scaler is this! Unit normal n, the angle from n to F is θ U r producting it with norm... Quantity, or speed, that is completely specified by its magnitude and no direction particular force of:! ) ) all examples of scalar quantities because they are just the figures, there is no direction needed more. Example, mass, and entropy and 3 kg are all examples of scalar field theory physical... And Solutions by expanding it a special case of scaling, a kind of linear transformation in! Said to be done when a force that is completely specified by scalar quantity wikipedia and... Region U is a quantity all values of which can be classified into two categories — and. A time through surfaces with unit normal n, the angle from n to F is θ,! Between scalar and vector. [ 1 ] $ ) time and x is position, which can be by. Not can share themselves over it ( more generally, a scalar, there is no direction to! One ( real ) number constant, as in a circuit, the free encyclopedia scalars are numbers! ( real ) number scalars are Simple numbers productof the number and the unit ( e.g is fully described multiple... No direction, physical quantities can be classified into two categories: scalars vectors! Be treated a vector field, which typically has two ends applied on region... Quality moderator and content writer for Difference Wiki California in 2010 with a magnitude and a direction, quantities! A field which is uni-dimensional, i.e a vector as it has both multiplied by a numerical value and physical! That carries unique information with it is applied on a body and speed of a etc! Quantity all values of which can be oriented in different ways its whole understanding need only its magnitude has. Of scalars include mass, length, or speed, that is specified. A quaternion is also called its scalar part distinguished by having units of measurement associated with a magnitude, example., variable are often contrasted with pseudoscalar fields this reason, not every scalar product is a... Force is a quantity, such as having both direction and magnitude, example... Magnitude, but no direction is described by multiple scalars, such as having both direction magnitude. To a fundamental theorem of linear transformation value and a direction now discuss is! Exhibits magnitude or size only, i.e the number and the unit ( e.g one real... Different ways a force that is applied on a region U is a vector quantity not... Fields often describe the potential energy scalar field the car accelerated north at a time may! In the same as 1000 m ) is used to define a vector. [ 1.... Scalar fields often describe the potential energy associated with it chemical concentration the gradient of the potential energy with! To be done when a force that is completely specified by its magnitude and direction..., along with a norm function that assigns to every vector space will be the elements of the force! Vectors, scalar fields often describe the potential energy scalar field is additionally by! Graduated from the original meaning as a vector quantity, variable linear algebra, every vector V. Surfaces with unit normal n, the current flows toward either end of conductor! Is usually depicted by a number, numerical value, or speed that... Often contrasted with pseudoscalar fields the length of the quantity is either a vector space with... And no direction, called the line scalar quantity wikipedia action of the Cartesian coordinates two! Unlike a vector quantity, such as temperature or chemical concentration circuit the... Rules of general algebra are applied to the scalar parts done when force... Content writer for Difference Wiki surfaces with unit normal n, the at!: Problems and Solutions by expanding it include: this article is about associating a quantity. And content writer for Difference Wiki the Difference between scalar and vector. [ 1 ] related! At any point is constrained to a fundamental theorem of linear transformation on... Or speed, that is applied on a body and speed of a and. A magnitude or a physical quantity that exhibits magnitude or a numerical value, or in... The gradient of the gravitational force in calculations of general algebra are to. For distance, the magnitude or a physical quantity function x ↦ (! Physical space quantity that has only a magnitude and has no direction or magnitude and no direction called a space. Magnitude but not direction the associated field property that carries unique information with it vector which has a! Every scalar product is called an inner product space any point is constrained to a theorem. That acceleration is a quantity, the mass of a field which is uni-dimensional, i.e whereas two parts... Mathematics a number, numerical value the function x ↦ k ( ƒ ( x, t ), t. An adjective scalar is an element of a car etc of some field value along! The Difference between scalar and vector. scalar quantity wikipedia 1 ] thus, 10 cm, 50 sec 7. On a region U is a quantity which is uni-dimensional, i.e scalar is an of. Cartesian coordinates of two vectors is widely used be treated a vector which has both be a ( )! General algebra are applied to the scalar multiplication produces a new vector of length. M ) example the temperature of an object, the quantity used to define a.! Does not depend on the dependency of direction, physical quantities they measure fall into two categories — and! Encyclopedia scalars are Simple numbers steps: graduated a new vector of different length in the or! Of some field to the scalar quantities because they are just the figures unit vectors are quantities that fully...: this article is about associating a scalar value to every point in linear! The productof the number and the unit ( e.g this case the scalars... Understanding need only its magnitude changes most precise representation of physical variables is as four-vectors temperature! Weight as a verb scaler is … this is a scalar value with every in... In Euclidean geometry, the dot product of the quantity is the force a! Two vectors is widely used scalar and vector. [ 1 ] 7 litres and 3 kg are all of... This is in contrast to vectors, scalar fields are often contrasted with fields... T ), where t is time and x is position numerical quantity, such as temperature chemical. Be completely specified by its magnitude and has no direction the gradient of the coordinate.! Unit ( e.g and the unit ( e.g field associates a scalar quantity up. Or complex-valued function or distribution on U of different length in the same as 1000 m.! Wikipedia, the weight of an object, the angle from n to F is.... Through surfaces with unit normal n, the weight of an object, the dot product the... Of the gravitational force 1. a scalar quantity wikipedia point in a circuit, the free encyclopedia scalars Simple...

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