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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Coordinate vector ： ウィキペディア英語版 Coordinate vector In linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers that describes the vector in terms of a particular ordered basis. Coordinates are always specified relative to an ordered basis. Bases and their associated coordinate representations let one realize vector spaces and linear transformations concretely as column vectors, row vectors, and matrices, hence are useful in calculations. The idea of a coordinate vector can also be used for infinite-dimensional vector spaces, as addressed below. == Definition == Let ''V'' be a vector space of dimension ''n'' over a field ''F'' and let :$B\; =\; \backslash$ be an ordered basis for ''V''. Then for every $v\; \backslash in\; V$ there is a unique linear combination of the basis vectors that equals ''v'': :$v\; =\; \backslash alpha\; \_1\; b\_1\; +\; \backslash alpha\; \_2\; b\_2\; +\; \backslash cdots\; +\; \backslash alpha\; \_n\; b\_n\; .$ The coordinate vector of ''v'' relative to ''B'' is the sequence of coordinates :$()\_B\; =\; (\backslash alpha\; \_1,\; \backslash alpha\; \_2,\; \backslash cdots,\; \backslash alpha\; \_n)\; .$ This is also called the ''representation of v with respect of B'', or the ''B representation of v''. The α-s are called the ''coordinates of v''. The order of the basis becomes important here, since it determines the order in which the coefficients are listed in the coordinate vector. Coordinate vectors of finite-dimensional vector spaces can be represented by matrices as column or row vectors. In the above notation, one can write :$()\_B\; =\; \backslash begin\; \backslash alpha\_1\; \backslash \backslash \; \backslash vdots\; \backslash \backslash \; \backslash alpha\_n\; \backslash end$ or : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Coordinate vector」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.