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:''This article is about the transpose of a matrix. For other uses, see Transposition'' :''Note that this article assumes that matrices are taken over a commutative ring. These results may not hold in the non-commutative case.'' In linear algebra, the transpose of a matrix A is another matrix AT (also written A′, Atr, tA or At) created by any one of the following equivalent actions: * reflect A over its main diagonal (which runs from top-left to bottom-right) to obtain AT * write the rows of A as the columns of AT * write the columns of A as the rows of AT Formally, the ''i'' th row, ''j'' th column element of AT is the ''j'' th row, ''i'' th column element of A: : If A is an matrix then AT is an matrix. The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley.〔Arthur Cayley (1858) ("A memoir on the theory of matrices," ) ''Philosophical Transactions of the Royal Society of London'', 148 : 17-37. The transpose (or "transposition") is defined on page 31.〕 == Examples == * * * 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「transpose」の詳細全文を読む スポンサード リンク
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