Manuals/calci/EXCHANGE
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle order} is the order of the Exchange matrix.
Description
- This function gives the exchange matrix of order 3.
- The exchange matrix is the square matrix of a permutation matrix.
- In this matrix the 1 elements reside on the counterdiagonal and all other elements are zero.
- It is a 'row-reversed' or 'column-reversed' version of the identity matrix.
- Suppose J is an nxn exchange matrix, then the elements of J are defined such that
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle J_{i,j}=\begin{cases} 1, j=n-i+1 \\ 0, j\neq n-i+1 \\ \end{cases}} .
- It is also called the reversal matrix,backward identity, or standard involutory permutation.
- The form of exchange matrices are
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle J_2=\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle J_3=\begin{pmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle J_n =\begin{pmatrix} 0 & 0 & \cdots & 0 & 0 & 1 \\ 0 & 0 & \cdots & 0 & 1 & 0 \\ 0 & 0 & \cdots & 1 & 0 & 0 \\ \vdots & \ddots & \vdots \\ 0 & 1 & \cdots & 0 & 0 & 0 \\ 1 & 0 & \cdots & 0 & 0 & 0 \\ \end{pmatrix}}
Examples
- 1.MATRIX("Exchange") =1
- 2.MATRIX("Exchange",3)
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
- 3.MATRIX("Exchange",6)
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |