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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 tensor product of quadratic forms ： ウィキペディア英語版 tensor product of quadratic forms The tensor product of quadratic forms is most easily understood when one views the quadratic forms as ''quadratic spaces''. So, if (''V'', ''q''1) and (''W'', ''q''2) are quadratic spaces, with ''V'',''W'' vector spaces, then the tensor product is a quadratic form ''q'' on the tensor product of vector spaces ''V'' ⊗ ''W''. It is defined in such a way that for $v\; \backslash otimes\; w\; \backslash in\; V\; \backslash otimes\; W$ we have $q(v\; \backslash otimes\; w)\; =\; q\_1(v)q\_2(w)$. In particular, if we have diagonalizations of our quadratic forms (which is always possible when the characteristic is not 2) such that :$q\_1\; \backslash cong\; \backslash langle\; a\_1,\; ...\; ,\; a\_n\; \backslash rangle$ :$q\_2\; \backslash cong\; \backslash langle\; b\_1,\; ...\; ,\; b\_m\; \backslash rangle$ then the tensor product has diagonalization :$q\_1\; \backslash otimes\; q\_2\; =\; q\; \backslash cong\; \backslash langle\; a\_1b\_1,\; a\_1b\_2,\; ...\; a\_1b\_m,\; a\_2b\_1,\; ...\; ,\; a\_2b\_m\; ,\; ...\; ,\; a\_nb\_1,\; ...\; a\_nb\_m\; \backslash rangle.$ 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「tensor product of quadratic forms」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.