Search Results for ""

Every dense linear order complete set without endpoints having at most omega disjoint intervals is order isomorphic to the continuum of real numbers, where omega is the set ...

The phrase "convergence in mean" is used in several branches of mathematics to refer to a number of different types of sequential convergence. In functional analysis, ...

Admitting an inverse. An object that is invertible is referred to as an invertible element in a monoid or a unit ring, or to a map, which admits an inverse map iff it is ...

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 ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a modular Hilbert algebra if A has an inner product <··> and a ...

Consider a set A_n={a_1,a_2,...,a_n} of n positive integer-denomination postage stamps sorted such that 1=a_1<a_2<...<a_n. Suppose they are to be used on an envelope with ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

R(X_1,...X_n)=sum_(i=1)^nH(X_i)-H(X_1,...,X_n), where H(x_i) is the entropy and H(X_1,...,X_n) is the joint entropy. Linear redundancy is defined as ...

A Lie group is called semisimple if its Lie algebra is semisimple. For example, the special linear group SL(n) and special orthogonal group SO(n) (over R or C) are ...

Let V and W be vector spaces over a field F, and let T:V->W be a linear transformation. Assuming the dimension of V is finite, then dim(V)=dim(Ker(T))+dim(Im(T)), where ...