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transpose : ウィキペディア英語版
transpose
:''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 ==

*\begin
1 & 2 \end^
1 \\
2 \end

*\begin
1 & 2 \\
3 & 4 \end^
1 & 3 \\
2 & 4 \end

*
\begin
1 & 2 \\
3 & 4 \\
5 & 6 \end^
1 & 3 & 5\\
2 & 4 & 6 \end


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



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