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Exchange matrix
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Exchange matrix : ウィキペディア英語版
Exchange matrix
In mathematics, especially linear algebra, the exchange matrix (also called the reversal matrix, backward identity, or standard involutory permutation) is a special case of a permutation matrix, where the 1 elements reside on the counterdiagonal and all other elements are zero. In other words, it is a 'row-reversed' or 'column-reversed' version of the identity matrix.〔.〕
:
J_=\begin
0 & 1 \\
1 & 0
\end;\quad J_=\begin
0 & 0 & 1 \\
0 & 1 & 0 \\
1 & 0 & 0
\end;
\quad J_=\begin
0 & 0 & \cdots & 0 & 0 & 1 \\
0 & 0 & \cdots & 0 & 1 & 0 \\
0 & 0 & \cdots & 1 & 0 & 0 \\
\vdots & \vdots & & \vdots & \vdots & \vdots \\
0 & 1 & \cdots & 0 & 0 & 0 \\
1 & 0 & \cdots & 0 & 0 & 0
\end.

==Definition==
If ''J'' is an ''n×n'' exchange matrix, then the elements of ''J'' are defined such that:
:J_ = \begin
1, & j = n - i + 1 \\
0, & j \ne n - i + 1\\
\end

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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