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Given a subalgebra A of the algebra B(H) of bounded linear transformations from a Hilbert space H onto itself, the vector v in H is a separating vector for A if the only ...

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 dual vector space to a real vector space V is the vector space of linear functions f:V->R, denoted V^*. In the dual of a complex vector space, the linear functions take ...

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 ...

An interior point method is a linear or nonlinear programming method (Forsgren et al. 2002) that achieves optimization by going through the middle of the solid defined by the ...

Ruffini's rule a shortcut method for dividing a polynomial by a linear factor of the form x-a which can be used in place of the standard long division algorithm. This method ...

The four following types of groups, 1. linear groups, 2. orthogonal groups, 3. symplectic groups, and 4. unitary groups, which were studied before more exotic types of groups ...

A vector v on a Hilbert space H is said to be cyclic if there exists some bounded linear operator T on H so that the set of orbits {T^iv}_(i=0)^infty={v,Tv,T^2v,...} is dense ...