n-dimensional space


Also found in: Wikipedia.

n-dimensional space

[′en di′men·shən·əl ′spās]
(mathematics)
A vector space whose basis has n vectors.
References in periodicals archive ?
Consequently, the data of disease area are linearly separable in the n-dimensional space and are overlapped partially (see Fig.
who studied the most efficient way to arrange spheres in n-dimensional space, a project that could have implications for supercooling liquids; Yale Fan, 18, of Beaverton, Ore.
Moon (1987) described fractal geometry more formally as a geometric property of a set of points in an n-dimensional space having a quality of selfsimilarity at different length scales and having a noninteger fractal dimension less than n.
Viewing input data as two sets of vectors in an n-dimensional space, an SVM will construct a separating hyperplane in that space, one which maximizes the margin between the two data sets.
Then they form a basis of < S > and n is called the dimension of < S >, which is then called an n-dimensional space.
For instance, the Cauchy-Riemann equations, which specify the regularity conditions for a complex-valued function to be analytic (expressible as a power series), generalize to the Lanczos equations in Minkowski spacetime, and then generalize further to the Nijenhuis tensor equations for holomorphic functions in n-dimensional space.
Here, in the chapter "Visible and Invisible Books: Hermetic Images in N-Dimensional Space," McGann sums up the position maintained by several contributors: literature's habitation in books remains a crucial part of any interpretation of a work.
This is especially important, as we continually assemble vectors and matrices to compute in n-dimensional space.
But that n-dimensional space must be defined somehow.
They explain the basic idea behind VDR by explaining, "By assuming that a variate is uniformly distributed on the contours or level curves of a given function in real n-dimensional space, and considering the density of the ordinate of the given function, the density of the original variate can be represented.
Indeed, any n-letter word can be plotted in n-dimensional space.
The main function of SOM networks is to map the input data from an n-dimensional space to a lower dimensional (usually one or two-dimensional) plot while maintaining the original topological relations.