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Originally, a product was and is still the result of the multiplication of two or more numbers.For example, 15 is the product of 3 and 5.The fundamental theorem of arithmetic states that every composite number is a product of prime numbers, that is unique up to the order of the factors.
The natural numbers 0 and 1 are trivial sum-product numbers for all , and all other sum-product numbers are nontrivial sum-product numbers. For example, the number 144 in base 10 is a sum-product number, because + + =, =, and =.
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
The product is one type of algebra for random variables: Related to the product distribution are the ratio distribution, sum distribution (see List of convolutions of probability distributions) and difference distribution. More generally, one may talk of combinations of sums, differences, products and ratios.
In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...
The direct sum and direct product are not isomorphic for infinite indices, where the elements of a direct sum are zero for all but for a finite number of entries. They are dual in the sense of category theory : the direct sum is the coproduct , while the direct product is the product.
The sum of a finite arithmetic progression is called an arithmetic series. ... Example 2. The product of the first 10 odd numbers (,,,,,) is given by = = ...
A double-dot product for matrices is the Frobenius inner product, which is analogous to the dot product on vectors. It is defined as the sum of the products of the corresponding components of two matrices and of the same size: : = ¯ = = ().