Manuals/calci/EXCHANGE

MATRIX("EXCHANGE",order)

• $order$ 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.

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

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