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In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
A much simpler result, stated in a section above, is that the variance of the product of zero-mean independent samples is equal to the product of their variances. Since the variance of each Normal sample is one, the variance of the product is also one. The product of two Gaussian samples is often confused with the product of two Gaussian PDFs.
In mathematics, the Lambert W function, also called the omega function or product logarithm, [1] is a multivalued function, namely the branches of the converse relation of the function f(w) = we w, where w is any complex number and e w is the exponential function. The function is named after Johann Lambert, who considered a related problem in 1758.
The product of non-negative integers can be defined with set theory using cardinal numbers or the Peano axioms. See below how to extend this to multiplying arbitrary integers, and then arbitrary rational numbers. The product of real numbers is defined in terms of products of rational numbers; see construction of the real numbers. [32]
The definition of matrix product requires that the entries belong to a semiring, and does not require multiplication of elements of the semiring to be commutative. In many applications, the matrix elements belong to a field, although the tropical semiring is also a common choice for graph shortest path problems. [15]
In mathematics, for a sequence of complex numbers a 1, a 2, a 3, ... the infinite product = = is defined to be the limit of the partial products a 1 a 2...a n as n increases without bound.
The product topology for infinite products has a twist, which has to do with being able to make all the projection maps continuous and to make all functions into the product continuous if and only if all its component functions are continuous (that is, to satisfy the categorical definition of product: the morphisms here are continuous functions).
If this product formula is changed to keep all but the last term, it would define a product of the same form, for a smaller factorial. This leads to a recurrence relation , according to which each value of the factorial function can be obtained by multiplying the previous value by n {\displaystyle n} : [ 21 ] n ! = n ⋅ ( n − 1 ...