Three Dimensional IMs - Index Matrices: Towards an Augmented Matrix Calculus - page 93

[2,1,3] -transposition

⎛ ⎞ [2 , 1 , 3]

H H

⎝ ⎠

=

L K

K L

a k i , l j , h g }] [ 2 , 1 , 3 ] =[ [ K , L , H , { L , K , H , { a l j , k i , h g }];

[2,3,1] -transposition

⎛
⎝

⎞
⎠

[2 , 3 , 1]

H K

=

L H

K L

a k i , l j , h g }] [ 2 , 3 , 1 ] =[ [ K , L , H , { L , H , K , { a l j , h g , k i }];

[3,1,2] -transposition

⎛
⎝

⎞
⎠

[3 , 1 , 2]

H L

=

L K

K H

a k i , l j , h g }] [ 3 , 1 , 2 ] =[ [ K , L , H , { H , K , L , { a h g , k i , l j }];