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Let H be a Hilbert space, B(H) the set of bounded linear operators from H to itself, T an operator on H, and sigma(T) the operator spectrum of T. Then if T in B(H) and T is ...

The image on the Riemann sphere of any circle under a complex rational mapping with numerator and denominator having degrees no more than n has length no longer than 2npi.

A square grid is a grid formed by tiling the plane regularly with squares.

The exploration of three-dimensional space from two-dimensional sections of projections of solid bodies.

The group of all nonsingular n×n stochastic matrices over a field F. It is denoted S(n,F). If p is prime and F is the finite field of order q=p^m, S(n,q) is written instead ...

The external (internal) similarity point of two fixed circles is the point at which all the circles homogeneously (nonhomogeneously) tangent to the fixed circles have the ...

The trace of a second-tensor rank tensor T is a scalar given by the contracted mixed tensor equal to T_i^i. The trace satisfies ...

In a category C, a terminal object is an object T in Ob(C) such that for any other object X in Ob(C), there is one, and only one morphism from X to T.

In an exterior algebra ^ V, a top-dimensional form has degree n where n=dimV. Any form of higher degree must be zero. For example, if V=R^4 then alpha=e_1 ^ e_2 ^ e_3 ^ e_4 ...

A totally imaginary field is a field with no real embeddings. A general number field K of degree n has s real embeddings (0<=s<=n) and 2t imaginary embeddings (0<=t<=n/2), ...