Product (mathematics)

In Mathematics , a product is the result of Multiplying , or an expression that identifies Factor s 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 Algebra s 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 Number s

Scalar Multiplication

The Dot Product and Cross Product are forms of multiplication of Vector s; the same as dot product or more general are the scalar product and the inner product; see also Inner Product Space

The product of Matrices ; see Matrix Multiplication .

The Pointwise Product of two Functions .

Products in Rings and Field s 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) .

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Product (mathematics)