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A linear real-valued function omega^1 of vectors v such that omega^1(v)|->R. Vectors (i.e., contravariant vectors or "kets" |psi>) and one-forms (i.e., covariant vectors or ...

A pullback is a general categorical operation appearing in a number of mathematical contexts, sometimes going under a different name. If T:V->W is a linear transformation ...

The square antiprism is the antiprism with square bases whose dual is the tetragonal trapezohedron. The square antiprism has 10 faces. The square antiprism with unit edge ...

A number of attractive 18-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

The polyhedron compound of the truncated cube and its dual, the small triakis octahedron. The compound can be constructed from a truncated cube of unit edge length by ...

A closed subspace of a Banach space X is called weakly complemented if the dual i^* of the natural embedding i:M↪X has a right inverse as a bounded operator. For example, the ...

A heptahedral graph is a polyhedral graph on seven nodes. There are 34 nonisomorphic heptahedral graphs, as first enumerated by Kirkman (1862-1863) and Hermes (1899ab, 1900, ...

If A, B, and C are three points on one line, D, E, and F are three points on another line, and AE meets BD at X, AF meets CD at Y, and BF meets CE at Z, then the three points ...

If two points A and A^' are inverse (sometimes called conjugate) with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to ...

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a ...