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Encyclopedia > Product (mathematics)

In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied. The order in which real or complex numbers are multiplied has no bearing on the product; this is known as the commutative law of multiplication. When matrices or members of various other associative algebras are multiplied the product usually depends on the order of the factors; in other words, matrix multiplication, and the multiplications in those other algebras, are non-commutative. For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... A result is the final consequence of a sequence of actions or events (broadly incidents and accidents) expressed qualitatively or quantitatively, being a loss, injury, disadvantage, advantage, gain, victory or simply a value. ... In mathematics, multiplication is an elementary arithmetic operation. ... In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder. ... In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ... A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram In mathematics, the complex numbers are the extension of the real numbers obtained by adjoining an imaginary unit, denoted i, which satisfies:[1] Every complex number can be... Example showing the commutativity of addition (3 + 2 = 2 + 3) For other uses, see Commute (disambiguation). ... In mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries), which may be numbers or, more generally, any abstract quantities that can be added and multiplied. ... In mathematics, an associative algebra is a vector space (or more generally, a module) which also allows the multiplication of vectors in a distributive and associative manner. ...


The product operator for the product of a series is denoted by the capital Greek letter Pi (in analogy to the use of the capital Sigma as summation symbol). In mathematics, multiplication is an elementary arithmetic operation. ...


Several products are considered in mathematics:

For other uses, see Number (disambiguation). ... 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 mathematics, the dot product, also known as the scalar product, is a binary operation which takes two vectors over the real numbers R and returns a real-valued scalar quantity. ... For the cross product in algebraic topology, see Künneth theorem. ... This article is about vectors that have a particular relation to the spatial coordinates. ... In mathematics, an inner product space is a vector space with additional structure, an inner product (also called a scalar product), which allows us to introduce geometrical notions such as angles and lengths of vectors. ... Outer product typically refers to the tensor product or to operations with similar cardinality such as exterior product. ... In mathematics, the exterior product or wedge product of vectors is an algebraic construction generalizing certain features of the cross product to higher dimensions. ... In mathematics, the interior product is a degree −1 derivation on the exterior algebra of differential forms on a smooth manifold. ... In mathematics, the tensor product, denoted by , may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules. ... In mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries), which may be numbers or, more generally, any abstract quantities that can be added and multiplied. ... In mathematics, matrix multiplication is the operation of multiplying a matrix with either a scalar or another matrix. ... The pointwise product of two functions is another function, obtained by multiplying the results of the two functions. ... This article is about functions in mathematics. ... In mathematics, a ring is an algebraic structure in which addition and multiplication are defined and have properties listed below. ... In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers. ... In mathematics, the Cartesian product is a direct product of sets. ... In mathematics, given a group G and two subgroups H and K of G, one can define the product of H and K, denoted by HK as the set of all elements of the form hk, for all h in H and k in K. In general HK is not... In abstract algebra, it is possible to combine several rings into one large product ring. ... In topology, the cartesian product of topological spaces is turned into a topological space in the following way. ... In probability theory, the Wick product named after physicist Gian-Carlo Wick, is a sort of product of the random variables, X1, ..., Xk, defined recursively as follows: (i. ... In probability theory, a random variable is a quantity whose values are random and to which a probability distribution is assigned. ... In category theory, one defines products to generalize constructions such as the cartesian product of sets, the product of groups, the product of rings and the product of topological spaces. ...

See also

In mathematics, multiplication is an elementary arithmetic operation. ... Sum redirects here. ... For other uses, see Pi (disambiguation) Pi (upper case Π, lower case π or ϖ) is the sixteenth letter of the Greek alphabet. ...

  Results from FactBites:
 
Product (mathematics) - MSN Encarta (101 words)
In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.
Product (mathematics), result of the multiplication of two or more quantities.
For example, 8 is the product of 2 × 4 and 30 is the product of 5 * 6.
PlanetMath: product (195 words)
The word product in mathematics generally means the result of some type of multiplication operation, i.e.
on vectors the scalar product, the vector product, the dyad product and the Hadamard product; on ideals the product of ideals;
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.
  More results at FactBites »

 
 

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