Length of a vector

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  • CLASSICAL GEOMETRY — LECTURE NOTES DANNY CALEGARI 1. A CRASH COURSE IN GROUP THEORY A group is an algebraic object which formalizes the mathematical notion which expresses the intuitive idea of symmetry. We start with an abstract definition. Definition 1.1. A group is a set G and an operation m : G × G → G called multiplication with the following properties: (1) m is associative. That is, for any a, b, c ∈ G, m(a, m(b, c)) = m(m(a, b), c) and the product can be written unambiguously as abc. (2) There is a unique element e ∈ G called the...

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  • Factored Statistical Machine Translation extends the Phrase Based SMT model by allowing each word to be a vector of factors. Experiments have shown effectiveness of many factors, including the Part of Speech tags in improving the grammaticality of the output. However, high quality part of speech taggers are not available in open domain for many languages.

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  • This paper suggests the efficient indexing method based on a concept vector space that is capable of representing the semantic content of a document. The two information measure, namely the information quantity and the information ratio, are defined to represent the degree of the semantic importance within a document. The proposed method is expected to compensate the limitations of term frequency based methods by exploiting related lexical items. Furthermore, with information ratio, this approach is independent of document length. ...

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  • A vector is a quantity that possesses both magnitude and direction. Examples of vector quantities are displacement, velocity, acceleration, and force. A vector quantity can be represented by an arrow drawn to scale. The length of the arrow is proportional to the magnitude of the vector quantity. The direction of the arrow represents the direction of the vector quantity.physics in general is the most scientific study of "physical" and "interaction".

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