You are here
Homeproduct
Primary tabs
product
The word product in mathematics generally means the result of some type of multiplication operation, i.e. of certain types of mapping $X\!\times\!X\rightarrow Y$; such operations are commonly distributive over the addition operation of $X$ if it is defined.
If $x_{1}$ and $x_{2}$ are two elements of the set $X$, giving the product $y\in Y$, then $x_{1}$ and $x_{2}$ are in general called the factors of this product.
Some most usual products are

the ring product (also in fields), especially the product of numbers and the product of square matrices;

on vectors the scalar product, the vector product, the dyad product and the Hadamard product; on ideals the product of ideals;

the Cartesian product, the direct products of various systems (not in connection with any additions).
Such kinds of product that are associative, allow to form a product of more than two factors, which is justified by the theorem in the entry general associativity. E.g. the usual product of the integers from 1 to $n$ is the factorial of $n$.
Mathematics Subject Classification
03E20 no label found Forums
 Planetary Bugs
 HS/Secondary
 University/Tertiary
 Graduate/Advanced
 Industry/Practice
 Research Topics
 LaTeX help
 Math Comptetitions
 Math History
 Math Humor
 PlanetMath Comments
 PlanetMath System Updates and News
 PlanetMath help
 PlanetMath.ORG
 Strategic Communications Development
 The Math Pub
 Testing messages (ignore)
 Other useful stuff
Recent Activity
new correction: Error in proof of Proposition 2 by alex2907
Jun 24
new question: A good question by Ron Castillo
Jun 23
new question: A trascendental number. by Ron Castillo
Jun 19
new question: Banach lattice valued Bochner integrals by math ias
Jun 13
new question: young tableau and young projectors by zmth