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A real quantity having a value less than zero (<0) is said to be negative. Negative numbers are denoted with a minus sign preceding the corresponding positive number, i.e., ...

Let H be a complex Hilbert space, and define a nest as a set N of closed subspaces of H satisfying the conditions: 1. 0,H in N, 2. If N_1,N_2 in N, then either N_1 subset= ...

A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

The pentatope graph is the skeleton of the pentatope, namely the complete graph K_5. It is sometimes also known as the Kuratowski graph (Nikolić et al. 2000, p. 281). Since ...

A group that coincides with its commutator subgroup. If G is a non-Abelian group, its commutator subgroup is a normal subgroup other than the trivial group. It follows that ...

The geometric centroid of a polyhedron composed of N triangular faces with vertices (a_i,b_i,c_i) can be computed using the curl theorem as x^_ = ...

The volume of a polyhedron composed of N triangular faces with vertices (a_i,b_i,c_i) can be computed using the curl theorem as V=1/6sum_(i=1)^Na_i·n_i, where the normal n_i ...

For a polynomial P=sum_(k=0)^na_kz^k, (1) several classes of norms are commonly defined. The l_p-norm is defined as ||P||_p=(sum_(k=0)^n|a_k|^p)^(1/p) (2) for p>=1, giving ...

The positive integers are the numbers 1, 2, 3, ... (OEIS A000027), sometimes called the counting numbers or natural numbers, denoted Z^+. They are the solution to the simple ...