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.