(Browder [8]) Let K be a nonempty compact convex subset of a topological
vector space. Let T be a map of K into [2.sup.K], where for each x [member of] K, T(x) is a nonempty convex subset of K.
(C) There is an isomorphism between the Clifford algebra Cl(d) in d-dimensions and the exterior algebra [LAMBDA] x M of cotangent bundle [T.sup.*] M over M [9, 10] (the space of the Clifford algebra Cl(d) is isomorphic, as a
vector space, to the
vector space of the exterior algebra [LAMBDA] x M.
founder and CEO John Garvey joins
Vector Space Systems as chief technology officer.
Micro satellite space launch enterprise
Vector Space Systems has secured more than USD1 million in angel funding at Space 2.0 in Silicon Valley, the company said.
They employed two different
vector space models to interpret word meaning--a basic bag-of-words model and a slightly simplified variant of the contextualization model of Thater et al.
Let (V,+,.) be any
vector space over a field K and let V (I) = < V [union] I > be a neutrosophic set generated by V and I.
Let V be a real
vector space of dimension n, equipped with a basis [DELTA] = {[[alpha].sub.1], [[alpha].sub.2], ..., [[alpha].sub.n]}.
Let X be real topological
vector space whose topology is induced by translation invariant metric d with the property
Definition 2 Let [F.sup.n] be a
vector space over the field F, and x, y [member of] [F.sup.n] where x = [x.sub.1],[x.sub.2] ...
Let V be a n dimensional
vector space over a field F and [sigma] a linear transformation on V.