Mathematical product - Definition

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
• The dot product and cross product are forms of multiplication of vectors.
• 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 cartesian product of sets,
  • the product of groups,
  • the product of rings,
  • the product of topological spaces,
  • for the general treatment, see product (category theory).