# Manuals/calci/EXCHANGE

MATRIX("EXCHANGE",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

.

• It is also called the reversal matrix,backward identity, or standard involutory permutation.
• The form of exchange matrices are

## 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