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Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

A projection matrix P is an n×n square matrix that gives a vector space projection from R^n to a subspace W. The columns of P are the projections of the standard basis ...

A topological space is second countable if it has a countable topological basis.

A complete metric is a metric in which every Cauchy sequence is convergent. A topological space with a complete metric is called a complete metric space.

The vectors +/-a_1, ..., +/-a_n in a three-space form a normalized eutactic star iff Tx=x for all x in the three-space.

A quantified system of real algebraic equations and inequalities in variables {x_1,...,x_n} is an expression QS=Q_1(y_1)Q_2(y_2)...Q_m(y_m)S(x_1,...,x_n;y_1,...,y_m), where Q ...

Surrogate data are artificially generated data which mimic statistical properties of real data. Isospectral surrogates have identical power spectra as real data but with ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

If a minimal surface is given by the equation z=f(x,y) and f has continuous first and second partial derivatives for all real x and y, then f is a plane.

The points on a line can be put into a one-to-one correspondence with the real numbers.