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Until the 19th century, linear algebra was introduced through systems of linear equations and modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general ( not limited to the finite- dimensional case), and conceptually simpler, although more abstract. A vector space over a field F ( often the field of the real mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense " related".
The objects correspond to mathematical abstractions called vertices ( also called nodes or points) and each of the related pairs of vertices is called an edge ( also called an arc or line).
Advanced Mathematics for Engineers Wolfgang Ertel translated by Elias Drotle and Richard Cubek October 1,. The fast Fourier transform ( FFT) is a discrete Fourier transform algorithm which reduces the number of computations needed for N points from 2N^ 2 to 2NlgN, where lg is the base- 2 logarithm. FFTs were first discussed by Cooley and Tukey ( 1965), although Gauss had actually described the critical factorization step as early as 1805 ( Bergland 1969, Strang 1993).
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