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. Matrix multiplication, and the multiplications in the other algebras, are non-commutative.

The product operator for the product of a sequence is denoted by the capital Greek letter Pi ∏ (in analogy to the use of the capital Sigma ∑ as summation symbol).

Several products are considered in mathematics:

• Products of the various classes of numbers

• • Wedge product or exterior product
  • Interior product
  • Tensor product
• The product of matrices and vectors; see matrix multiplication, dot product, Kronecker product.
• The pointwise product of two functions.
• A function's product integral (as a continuous equivalent to the product of a sequence or the multiplicative version of the (normal/standard/additive) integral. The product integral is also known as "continuous product" or "multiplical".
• 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 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).

See also

• Pi (letter)
• Iterated binary operation