Computers understand very little of the meaning of human language. This profoundly limits our ability to give instructions to computers, the ability of computers to explain their actions to us, and the ability of computers to analyse and process text. Vector space models (VSMs) of semantics

this document has been paraphrased from miscellaneous sections of referemces [1, 2, 3], and other sources. If the brief descriptions here are not sufficient, the reader is referred to these sources for more complete coverage. 1.1 Why study vector spaces before signal processing?

This paper considers ordered vector spaces with arbitrary closed cones and establishes a number of characterization results with applications to monotone comparative statics (Topkis (1978), Topkis (1998), Milgrom and Shannon (1994)). By appealing to the fundamental theorem of calculus

We propose two novel model architectures for computing continuous vector representations of words from very large data sets. The quality of these representations is measured in a word similarity task, and the results are compared to the previ-ously best performing techniques based on different

We prove a vector space analog of a version of the Kruskal-Katona theorem due to Lovász. We apply this result to extend Frankl’s theorem on r-wise intersecting families to vector spaces. In particular, we obtain a short new proof of the Erdős-Ko-Rado theorem for vector spaces.

Abstract: A Smarandache multi-space is a union of n spaces A1,A2, · · ·,An with some additional conditions holding. Combining Smarandache multispaces with linear vector spaces in classical linear algebra, the conception of multi-vector spaces is introduced. Some characteristics of a multi-vector

there is no shortage of textual materials on a particular topic, procedures for indexing or extracting the knowledge or conceptual information contained in them can be lacking. Recently developed information retrieval technologies are based on the concept of a vector space. Data are modeled as a matrix, and a user’s

Abstract. In this paper we determine what properties an approach struc-ture has to fulfil for it to concord well with a vector space structure. Not surprisingly these conditions are more subtle than those for a topology. That the conditions we impose are the right ones follows mainly from the good

In this paper, we introduce and study semitopological vector spaces. The goal is to provide an efficient base for developing the theory of extrafunction spaces in an abstract setting of algebraic systems and topological spaces. Semitopological vector spaces are more general than conventional

Abstract: A metric vector space is asymptotically metrically normable (AMN) if there exists a norm asymptotically isometric to the distance. We prove that AMN vector spaces are rigid in the class of metric vector spaces under asymptotically isometric perturbations. This result follows from a