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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 Outer product ： ウィキペディア英語版 Outer product :''For "outer product" in geometric algebra, see Exterior algebra.'' In linear algebra, the term outer product typically refers to the tensor product of two vectors. The result of applying the outer product to a pair of coordinate vectors is a matrix. The name contrasts with the inner product, which takes as input a pair of vectors and produces a scalar. The outer product of vectors can be also regarded as a special case of the Kronecker product of matrices. Some authors use the expression "outer product of tensors" as a synonym of "tensor product". The outer product is also a higher-order function in some computer programming languages such as R, APL, and Mathematica. ==Definition (matrix multiplication)== (詳細はcolumn vector and v as a column vector (which makes vT a row vector).〔Linear Algebra (4th Edition), S. Lipschutz, M. Lipson, Schaum’s Outlines, McGraw Hill (USA), 2009, ISBN 978-0-07-154352-1〕 For instance, if and , then :$\backslash mathbf\; \backslash otimes\; \backslash mathbf\; =\; \backslash mathbf\; \backslash mathbf^\backslash mathrm\; =$ \beginu_1 \\ u_2 \\ u_3 \\ u_4\end \beginv_1 & v_2 & v_3\end = \beginu_1v_1 & u_1v_2 & u_1v_3 \\ u_2v_1 & u_2v_2 & u_2v_3 \\ u_3v_1 & u_3v_2 & u_3v_3 \\ u_4v_1 & u_4v_2 & u_4v_3\end. Or in index notation: :$(\backslash mathbf\; \backslash mathbf^\backslash mathrm)\_=u\_iv\_j$ For complex vectors, it is customary to use the conjugate transpose of v (denoted vH): :$\backslash mathbf\; \backslash otimes\; \backslash mathbf\; =\; \backslash mathbf\; \backslash mathbf^\backslash mathrm.$ 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「Outer product」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.