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Given a contravariant basis {e^->_1,...,e^->_n}, its dual covariant basis is given by e^->^alpha·e^->_beta=g(e^->^alpha,e^->_beta)=delta_beta^alpha, where g is the metric and ...

A symbol used to represent the point and space groups (e.g., 2/m3^_). Some symbols have abbreviated form. The equivalence between Hermann-Mauguin symbols (a.k.a. ...

A bounded operator T:V->W between two Banach spaces satisfies the inequality ||Tv||<=C||v||, (1) where C is a constant independent of the choice of v in V. The inequality is ...

A set S is discrete in a larger topological space X if every point x in S has a neighborhood U such that S intersection U={x}. The points of S are then said to be isolated ...

The hemicube, which might also be called the square hemiprism, is a simple solid that serves as an example of one of the two topological classes of convex hexahedron having 7 ...

The tensor product between modules A and B is a more general notion than the vector space tensor product. In this case, we replace "scalars" by a ring R. The familiar ...

A regular skew polyhedron is a polyhedron whose faces and vertex figures are regular skew polygons. There are only three regular skew polyhedra in Euclidean three-space ...

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 ...

The delta function is a generalized function that can be defined as the limit of a class of delta sequences. The delta function is sometimes called "Dirac's delta function" ...

Bicentric perspective is the study of the projection of 3D space from a pair of fiducial points instead of a single one, the latter of which may be called "centric" or ...