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A linear transformation A:R^n->R^n is hyperbolic if none of its eigenvalues has modulus 1. This means that R^n can be written as a direct sum of two A-invariant subspaces E^s ...

A generalization of an ordinary two-dimensional surface embedded in three-dimensional space to an (n-1)-dimensional surface embedded in n-dimensional space. A hypersurface is ...

Two variates A and B are statistically independent iff the conditional probability P(A|B) of A given B satisfies P(A|B)=P(A), (1) in which case the probability of A and B is ...

The L^2-inner product of two real functions f and g on a measure space X with respect to the measure mu is given by <f,g>_(L^2)=int_Xfgdmu, sometimes also called the bracket ...

In two-dimensional bipolar coordinates, Laplace's equation is ((coshv-cosu)^2)/(a^2)((partialF^2)/(partialu^2)+(partialF^2)/(partialv^2))=0, which simplifies to ...

The degree of a graph vertex of a graph is the number of graph edges which touch the graph vertex, also called the local degree. The graph vertex degree of a point A in a ...

The two integrals involving Bessel functions of the first kind given by (alpha^2-beta^2)intxJ_n(alphax)J_n(betax)dx ...

The MacBeath circle, a term coined here for the first time, is the circumcircle of the MacBeath triangle. It has a fairly complicated radius, center function, and circle ...

Denote the sum of two matrices A and B (of the same dimensions) by C=A+B. The sum is defined by adding entries with the same indices c_(ij)=a_(ij)+b_(ij) over all i and j. ...

If two square n×n matrices A and B are simultaneously upper triangularizable by similarity transforms, then there is an ordering a_1, ..., a_n of the eigenvalues of A and ...