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If an airplane's altitude at time t is a(t), and the air pressure at altitude x is p(x), then (p ∘ a)(t) is the pressure around the plane at time t. Function defined on finite sets which change the order of their elements such as permutations can be composed on the same set, this being composition of permutations.
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
In abstract algebra, a decomposition of a module is a way to write a module as a direct sum of modules.A type of a decomposition is often used to define or characterize modules: for example, a semisimple module is a module that has a decomposition into simple modules.
The Jordan–Chevalley decomposition of an element in algebraic group as a product of semisimple and unipotent elements; The Bruhat decomposition = of a semisimple algebraic group into double cosets of a Borel subgroup can be regarded as a generalization of the principle of Gauss–Jordan elimination, which generically writes a matrix as the product of an upper triangular matrix with a lower ...
In mathematics, the term cycle decomposition can mean: . Cycle decomposition (graph theory), a partitioning of the vertices of a graph into subsets, such that the vertices in each subset lie on a cycle
The strictly positive values in the Schmidt decomposition of are its Schmidt coefficients, or Schmidt numbers. The total number of Schmidt coefficients of w {\displaystyle w} , counted with multiplicity, is called its Schmidt rank .
The Wild Numbers is a mathematical fiction in the form of a short novel by Philibert Schogt, a Dutch philosopher and mathematician. It was first published in Dutch (as "De wilde getallen") in 1998 and an English translation appeared in 2000. [1] Through this work the author is trying to provide insights to the workings of a mathematics-obsessed ...
Demonstration, with Cuisenaire rods, of the first four highly composite numbers: 1, 2, 4, 6. A highly composite number is a positive integer that has more divisors than all smaller positive integers. If d(n) denotes the number of divisors of a positive integer n, then a positive integer N is highly composite if d(N) > d(n) for all n < N.