product

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OR:

Product may refer to:

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

# Mathematics

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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

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Direct product In mathematics, one can often define a direct product of objects already known, giving a new one. This generalizes the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one ta ...

### Set theory

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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

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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 on ...
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Semidirect product In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product. There are two closely related concepts of semidirect product: * an ''inner'' semidirect product is a particular way in ...
* Product of group subsets *
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 ...
* Free product * Zappa–Szép product (or knit product), a generalization of the direct and semidirect products

### Ring theory

* Product of rings * Ideal operations, for product of ideals

### Linear algebra

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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 vecto ...
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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 ...
* 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 ...
*
Exterior product In mathematics, specifically in general topology, topology, the interior of a subset of a topological space is the Union (set theory), union of all subsets of that are Open set, open in . A point that is in the interior of is an interior point ...
or wedge product * Multiplication of vectors: **
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 algeb ...
**
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 d ...
** Seven-dimensional cross product **
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 \otime ...

## Topology

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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-seemi ...

### Algebraic topology

* Cap product * Cup product * Slant product

### Homotopy theory

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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 id ...
*
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 ...
(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 an ...
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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 ring ...
, a generalization of mathematical products * Fibre product or pullback ** Coproduct or pushout

## Probability theory

* Wick product of random variables

* Graph product

# 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 independe ...

# Other uses

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