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For example, 15 is a composite number because 15 = 3 · 5, but 7 is a prime number because it cannot be decomposed in this way. If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4) .
Decomposing a number into = +, and then applying to and an order-preserving map from the Moser–de Bruijn sequence to the integers (by replacing the powers of four in each number by the corresponding powers of two) gives a bijection from non-negative integers to ordered pairs of non-negative integers.
If two matrices of order n can be multiplied in time M(n), where M(n) ≥ n a for some a > 2, then an LU decomposition can be computed in time O(M(n)). [16] This means, for example, that an O(n 2.376) algorithm exists based on the Coppersmith–Winograd algorithm.
Applicable to: square, hermitian, positive definite matrix Decomposition: =, where is upper triangular with real positive diagonal entries Comment: if the matrix is Hermitian and positive semi-definite, then it has a decomposition of the form = if the diagonal entries of are allowed to be zero
A decomposition paradigm in computer programming is a strategy for organizing a program as a number of parts, and usually implies a specific way to organize a program text. Typically the aim of using a decomposition paradigm is to optimize some metric related to program complexity, for example a program's modularity or its maintainability.
For operators of fixed order the possible Loewy decompositions, differing by the number and the order of factors, may be listed explicitly; some of the factors may contain parameters. Each alternative is called a type of Loewy decomposition. The complete answer for = is detailed in the following corollary to the above theorem. [3]
CSGO says players should avoid the notoriously unlucky number 13, which has been drawn only 51 times in 8 years. The bottom 10, unluckiest numbers with the fewest frequency are: 13. 49. 34. 29. 26 ...
Algorithms are known for decomposing univariate polynomials in polynomial time. Polynomials which are decomposable in this way are composite polynomials; those which are not are indecomposable polynomials or sometimes prime polynomials [1] (not to be confused with irreducible polynomials, which cannot be factored into products of polynomials).
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