Product (mathematics)
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For other senses of this word, see product.
In the a mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied. The order in 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.
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
- The product of matrices and vectors; see matrix multiplication, dot product, Kronecker product.
- 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,
- the Wick product of random variables.
- For the general treatment, see product (category theory).
