GROUP INVAKIANCE OR TOTAL SYMMETRY 



1447 



responding matrix operations will not change the transmission matrix 

 aside from possibly reordering the rows. In other words, it should b^ 

 possible to reorder the rows of the modified transmission matrix to re- 

 gain the original transmission matrix. The matrices of Table 1(a) and 

 (b) are identical except for the interchange of the 1 and 2 and the 9 

 and 10 rows. It is not possible to make the matrix of Table 1(c) identical 

 with that of Table 1(a) by reordering rows; therefore the operation of 

 priming the x^ and .r4 variables does not leave the transmission T = 

 J] (0, 1, 2, 9, 10, 11) michanged. 



If interchanging two columns of a matrix does not change the matrix 

 aside from rearranging the rows, then the columns which were inter- 

 changed must both contain the same number of I's (and O's). This must 



Table II — Partitioning of the Standard Matrix for 

 2^ = Z (4, 5, 7, 8, 9, 11, 30, 33, 49) 



(a) Transmission Matrix 



(b) Standard Matrix for (a) Matrix 



Weight 

 1 

 1 

 1 



2 

 2 



2 

 2 

 2 



(c) Second Partitioning of 

 rows for (b) matrix 



(d) Final Partitioning 

 for (b) matrix 



