LYCOS RETRIEVER 
Vector Space: Vector Spaces
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The vector space model procedure can be divided in to three stages. The first stage is the document indexing where content bearing terms are extracted from the document text. The second stage is the weighting of the indexed terms to enhance retrieval of document relevant to the user. The last stage ranks the document with respect to the query according to a similarity measure.
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Vector Space worked closely with economists at the firm to identify key factors driving growth, revenue and variable cost. Once comfortable with a workable set of functions, VS consultants proposed a comprehensive model.
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The vector space model has been widely used in the traditional IR field [11,12]. Most search engines ... use similarity measures based on this model to rank Web documents. The model creates a space in which both documents and queries are represented by vectors. For a fixed collection of documents, an-dimensional vector is generated for each document and each query from sets of terms with associated weights, where is the number of unique terms in the document collection. Then, a vector similarity function, such as the inner product, can be used to compute the similarity between a document and a query.
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The purpose of this book is to present a version of multivariate statistical theory in which vector space and invariance methods replace, to a large extent, more traditional multivariate methods. The book is a text. Over the past ten years, various versions have been used for graduate multivariate courses at the University of Chicago, the University of Copenhagen, and the University of Minnesota. Designed for a one year lecture course or for independent study, the book contains a full complement of problems and problem solutions.
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Given a vector space V, a nonempty subset W of V that is closed under addition and scalar multiplication is called a subspace of V. Subspaces of V are vector spaces (over the same field) in their own right. The intersection of all subspaces containing a given set of vectors is called its span; if no vector can be removed without changing the span, the set is said to be linearly independent. A linearly independent set whose span is V is called a basis for V.
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One obvious example of a vector space is a Euclidean space. Vectors are arrows from the origin to some point in the space - and so they can be represented as ordered tuples. So for example, ℜ3 is the three-dimensional euclidean space; points (x,y,z) are vectors. Adding two vectors (a,b,c)+(d,e,f)=(a+d,b+e,c+f); and scalar multiplication x*(a,b,c)=(x*a,x*b,x*c).
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Vector Spaces