Difference between revisions of "Manuals/calci/EXCHANGE"

Revision as of 10:39, 27 April 2015

MATRIX("EXCHANGE",order)

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.

$J_{i,j}={\begin{cases}1,j=n-i+1\\0,j\neq n-i+1\\\end{cases}}$ .

It is also called the reversal matrix,backward identity, or standard involutory permutation.
The form of exchange matrices are J2=();J3=(); and so on.

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-<div style="font-size:30px">'''EXCHANGE'''</div><br/>
+<div style="font-size:30px">'''MATRIX("EXCHANGE",order)'''</div><br/>
+*<math>order</math> 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.
+<math> J_{i,j}=\begin{cases}
+,  j=n-i+1 \\
+, j\neq n-i+1 \\
+\end{cases}</math>.
+*It is also called the reversal matrix,backward identity, or standard involutory permutation.
+*The form of exchange matrices are J2=();J3=(); and so on.