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")
0 0 1
0 1 0
1 0 0
  • 2.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

See Also

References