Product may refer to:

Business

Product (business) In marketing, a product is an object, or system, or service made available for consumer use as of the consumer demand; it is anything that can be offered to a market to satisfy the desire or need of a customer. In retailing, products are often ...

, 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 ba ...

, a deliverable or set of deliverables that contribute to a business solution

Mathematics

Product (mathematics) In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called ''factors''. For example, 30 is the product of 6 and 5 (the result of multiplication), and x\cd ...

Algebra

* Direct product

Set theory

Cartesian product In mathematics, specifically set theory, the Cartesian product of two sets ''A'' and ''B'', denoted ''A''×''B'', is the set of all ordered pairs where ''a'' is in ''A'' and ''b'' is in ''B''. In terms of set-builder notation, that is : A\ti ...

of sets

Group theory

Direct product of groups In mathematics, specifically in group theory, the direct product is an operation that takes two groups and and constructs a new group, usually denoted . This operation is the group-theoretic analogue of the Cartesian product of sets and is one ...

* Semidirect product *

Product of group subsets In mathematics, one can define a product of group subsets in a natural way. If ''S'' and ''T'' are subsets of a group ''G'', then their product is the subset of ''G'' defined by :ST = \. The subsets ''S'' and ''T'' need not be subgroups for this pro ...

Wreath product In group theory, the wreath product is a special combination of two groups based on the semidirect product. It is formed by the action of one group on many copies of another group, somewhat analogous to exponentiation. Wreath products are used i ...

Free product In mathematics, specifically group theory, the free product is an operation that takes two groups ''G'' and ''H'' and constructs a new The result contains both ''G'' and ''H'' as subgroups, is generated by the elements of these subgroups, and is ...

Zappa–Szép product In mathematics, especially group theory, the Zappa–Szép product (also known as the Zappa–Rédei–Szép product, general product, knit product, exact factorization or bicrossed product) describes a way in which a group can be constructed fro ...

(or knit product), a generalization of the direct and semidirect products

Ring theory

Product of rings In mathematics, a product of rings or direct product of rings is a ring that is formed by the Cartesian product of the underlying sets of several rings (possibly an infinity), equipped with componentwise operations. It is a direct product in th ...

* Ideal operations, for product of ideals

Linear algebra

Scalar multiplication In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra). In common geometrical contexts, scalar multiplication of a real Euclidean vector by ...

Matrix multiplication In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the s ...

* Inner product, on an

inner product space In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often den ...

Exterior product In mathematics, specifically in topology, the interior of a subset of a topological space is the union of all subsets of that are open in . A point that is in the interior of is an interior point of . The interior of is the complement of th ...

or wedge product *

Multiplication of vectors In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles: * Dot product – also known as the "scalar product", a binary operation that takes two vector ...

: **

Dot product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an algebra ...

Cross product In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is ...

Seven-dimensional cross product In mathematics, the seven-dimensional cross product is a bilinear operation on vectors in seven-dimensional Euclidean space. It assigns to any two vectors a, b in a vector also in . Like the cross product in three dimensions, the seven-dim ...

Triple product In geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector- ...

, in vector calculus *

Tensor product In mathematics, the tensor product V \otimes W of two vector spaces and (over the same field) is a vector space to which is associated a bilinear map V\times W \to V\otimes W that maps a pair (v,w),\ v\in V, w\in W to an element of V \otimes W ...

Topology

Product topology In topology and related areas of mathematics, a product space is the Cartesian product of a family of topological spaces equipped with a natural topology called the product topology. This topology differs from another, perhaps more natural-seemin ...

Algebraic topology

Cap product In algebraic topology the cap product is a method of adjoining a 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 by Eduard Čech in 1936, an ...

Cup product In mathematics, specifically in algebraic topology, the cup product is a method of adjoining two cocycles of degree ''p'' and ''q'' to form a composite cocycle of degree ''p'' + ''q''. This defines an associative (and distributive) graded commutat ...

Slant product In algebraic topology the cap product is a method of adjoining a 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 by Eduard Čech in 1936, an ...

Homotopy theory

Smash product In topology, a branch of mathematics, the smash product of two pointed spaces (i.e. topological spaces with distinguished basepoints) (''X,'' ''x''0) and (''Y'', ''y''0) is the quotient of the product space ''X'' × ''Y'' under the ide ...

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 the qu ...

(or wedge product)

Category theory

* Internal product, in a

monoidal category In mathematics, a monoidal category (or tensor category) is a category \mathbf C equipped with a bifunctor :\otimes : \mathbf \times \mathbf \to \mathbf that is associative up to a natural isomorphism, and an object ''I'' that is both a left and r ...

Product (category theory) In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the Cartesian product of sets, the direct product of groups or rings, ...

, 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 ...

or pullback ** Coproduct or

pushout A ''pushout'' is a student who leaves their school before graduation, through the encouragement of the school. A student who leaves of their own accord (e.g., to work or care for a child), rather than through the action of the school, is consider ...

Probability theory

Wick product In probability theory, the Wick product is a particular way of defining an adjusted product of a set of random variables. In the lowest order product the adjustment corresponds to subtracting off the mean value, to leave a result whose mean is zero. ...

of random variables

Graph theory

Graph product In graph theory, a graph product is a binary operation on Graph (discrete mathematics), graphs. Specifically, it is an operation that takes two graphs and and produces a graph with the following properties: * The vertex (graph theory), vertex ...

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 Manchester music scene, the independen ...

Other uses

Product (chemistry) Products are the species formed from chemical reactions. During a chemical reaction, reactants are transformed into products after passing through a high energy transition state. This process results in the consumption of the reactants. It can be a ...

, the species formed from chemical reactions *

Hairstyling product Hairstyle products are used to change the texture and/or shape of hair. History Hairstyling products have had a significant impact on the creation of various hairstyles and trends throughout history. For the ancient Egyptians, physical appearanc ...

, such as hairspray or hair gel, generally referred to as simply "product"