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A collection of subsets of a topological space that is contained in a basis of the topology and can be completed to a basis when adding all finite intersections of the ...

An ordered vector basisv_1,...,v_n for a finite-dimensional vector space V defines an orientation. Another basis w_i=Av_i gives the same orientation if the matrix A has a ...

Smarandache sequences are any of a number of simply generated integer sequences resembling those considered in published works by Smarandache such as the consecutive number ...

A symmetric bilinear form on a vector space V is a bilinear function Q:V×V->R (1) which satisfies Q(v,w)=Q(w,v). For example, if A is a n×n symmetric matrix, then ...

A square matrix U is a unitary matrix if U^(H)=U^(-1), (1) where U^(H) denotes the conjugate transpose and U^(-1) is the matrix inverse. For example, A=[2^(-1/2) 2^(-1/2) 0; ...

The term metric signature refers to the signature of a metric tensor g=g_(ij) on a smooth manifold M, a tool which quantifies the numbers of positive, zero, and negative ...

An abstract vector space of dimension n over a field k is the set of all formal expressions a_1v_1+a_2v_2+...+a_nv_n, (1) where {v_1,v_2,...,v_n} is a given set of n objects ...

The icosahedral group I_h is the group of symmetries of the icosahedron and dodecahedron having order 120, equivalent to the group direct product A_5×Z_2 of the alternating ...

A topology that is "potentially" a metric topology, in the sense that one can define a suitable metric that induces it. The word "potentially" here means that although the ...

O_h is the point group of symmetries of the octahedron having order 48 that includes inversion. It is also the symmetry group of the cube, cuboctahedron, and truncated ...