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Product may refer to:


Business

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Product (business) In marketing, a product is an object or system made available for consumer use; it is anything that can be offered to a Market (economics), market to satisfy the desire or need of a customer. In retailing, products are often referred to as ''Me ...
, an item that serves as a solution to a specific consumer problem. *
Product (project management) {{more citations needed, date=January 2021 In project management under the PRINCE2 methodology, a product breakdown structure (PBS) is a tool for analysing, documenting and communicating the outcomes of a project, and forms part of the product base ...
, a deliverable or set of deliverables that contribute to a business solution


Mathematics

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Product (mathematics) In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no gene ...


Algebra

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Direct productIn mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ha ...


Set theory

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Cartesian product In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...
of sets


Group theory

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Direct product of groups In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
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Semidirect product In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...
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Product of group subsetsIn mathematics, one can define a product of group subsets in a natural way. If ''S'' and ''T'' are subsets of a group (mathematics), group ''G'', then their product is the subset of ''G'' defined by :ST = \. The subsets ''S'' and ''T'' need not be su ...
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Wreath product In group theory The popular puzzle Rubik's cube invented in 1974 by Ernő Rubik has been used as an illustration of permutation group">Ernő_Rubik.html" ;"title="Rubik's cube invented in 1974 by Ernő Rubik">Rubik's cube invented in 1974 by Er ...
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Free product In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It h ...
* Zappa–Szép product (or knit product), a generalization of the direct and semidirect products


Ring theory

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Product of rings In mathematics, it is possible to combine several ring (mathematics), rings into one large product ring. This is done by giving the Cartesian product of a (possibly infinite) family of rings coordinatewise addition and multiplication. The resulting ...
* Ideal operations, for product of
ideals Ideal may refer to: Philosophy * Ideal (ethics), values that one actively pursues as goals * Platonic ideal, a philosophical idea of trueness of form, associated with Plato Mathematics * Ideal (ring theory), special subsets of a ring considered ...


Linear algebra

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Scalar multiplication 250px, The scalar multiplications −a and 2a of a vector a In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry ...

Scalar multiplication
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Matrix multiplication In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and t ...

Matrix multiplication
* Inner product, on an
inner product space In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...
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Exterior product In topology s, which have only one surface and one edge, are a kind of object studied in topology. In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical struc ...
or wedge product *
Multiplication of vectorsIn mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ha ...
: **
Dot product In mathematics, the dot product or scalar productThe term ''scalar product'' is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space. is an algebraic operation that takes two equal-length seque ...
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Cross product In , the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a on two s in a three-dimensional (named here E), and is denoted by the symbol \times. Given two and , the cross produc ...

Cross product
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Seven-dimensional cross productIn mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ha ...
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Triple product In geometry and algebra, the triple product is a product of three 3-dimension (vector space), dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, ...
, in vector calculus *
Tensor product In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...

Tensor product


Topology

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Product topology Product may refer to: Business * Product (business) In marketing, a product is an object or system made available for consumer use; it is anything that can be offered to a Market (economics), market to satisfy the desire or need of a customer ...


Algebraic topology

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Cap product In algebraic topology the cap product is a method of adjoining a chain (algebraic topology), chain of degree ''p'' with a cochain of degree ''q'', such that ''q'' ≤ ''p'', to form a composite chain of degree ''p'' − ''q''. It was introduced b ...
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Cup productIn mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ha ...
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Slant product In algebraic topology the cap product is a method of adjoining a chain (algebraic topology), chain of degree ''p'' with a cochain of degree ''q'', such that ''q'' ≤ ''p'', to form a composite chain of degree ''p'' − ''q''. It was introduced b ...


Homotopy theory

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Smash product Smash may refer to: People * Smash (wrestler) (born 1959), professional wrestler * Moondog Rex, another professional wrestler who briefly wrestled as the original Smash, before being replaced by the above. * DJ Smash, DJ and music producer Ar ...
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Wedge sum In topology, the wedge sum is a "one-point union" of a family of topological spaces. Specifically, if ''X'' and ''Y'' are pointed spaces (i.e. topological spaces with distinguished basepoints ''x''0 and ''y''0) the wedge sum of ''X'' and ''Y'' is th ...
(or wedge product)


Category theory

* Internal product, in a
monoidal category In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It h ...
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Product (category theory) In category theory Category theory formalizes mathematical structure and its concepts in terms of a Graph labeling, labeled directed graph called a ''Category (mathematics), category'', whose nodes are called ''objects'', and whose labelled d ...
, a generalization of mathematical products *
Fibre product In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit (category theory), limit of a diagram (category theory), diagram consisting of two morphisms an ...
or pullback ** Coproduct or pushout


Probability theory

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Wick productIn probability theory, the Wick product is a particular way of defining an adjusted product (mathematics), product of a set of random variables. In the lowest order product the adjustment corresponds to subtracting off the mean value, to leave a resu ...
of random variables


Graph theory

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Graph productIn mathematics, a graph product is a binary operation on Graph (discrete mathematics), graphs. Specifically, it is an operation that takes two graphs ''G''1 and ''G''2 and produces a graph ''H'' with the following properties: * The vertex (graph the ...


Music

* ''Product'' (Brand X album), 1979 * ''Product'' (De Press album), 1982 * ''Product'' (Sophie album), 2015 * ''Product'', a three-CD compilation set by
Buzzcocks Buzzcocks are an English punk rock band formed in Bolton, England in 1976 by singer-songwriter-guitarist Pete Shelley and singer-songwriter Howard Devoto. They are regarded as a seminal influence on the Music of Manchester, Manchester music sc ...

Buzzcocks


Other uses

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Product (chemistry) Products are the species formed from chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substance is a form of matter In classical physics and genera ...
, the species formed from chemical reactions * Hairstyling product, such as hairspray or hair gel, generally referred to as simply "product"


See also

* Production (disambiguation) {{disambiguation