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.
Several products are considered in mathematics:

★ Products of the various classes of numbers

★ scalar multiplication

★ The dot product and cross product are forms of multiplication of vectors. Related products are:

★
★ Inner product

★
★ Outer product

★
★ Wedge product or exterior product

★
★ Interior product

★
★ Tensor product

★ The product of matrices; see matrix multiplication.

★ The pointwise product of two functions.

★ Products in rings and fields of many kinds.

★ It is often possible to form the product of two (or more) mathematical objects to form another object of the same kind, e.g.

★
★ the Product of a series (Capital pi)

★
★ the cartesian product of sets,

★
★ the product of groups,

★
★ the product of rings,

★
★ the product of topological spaces,

★
★ the Wick product of random variables,

★
★ for the general treatment, see product (category theory).

Contents

See also

See also

★ Multiplication

★ Summation

★ Pi (letter)