Table 6:

The desired form of blocks $X_{ij}^{(k,m)}$ of $X^{(k,m)}$, after averaging inter-class rotations (lemma 1)

$\text{(a) }{a}_i=a_j$					$\text{(b) }{a}_i\ne a_j$
$X^{(k,m)}$	$\mathit{m}=0$	$\mathit{m}=1$	$\cdots$	$\mathit{m}=\mathit{M}-1$	$X^{(k,m)}$	$\mathit{m}=0$	$\mathit{m}=1$	$\cdots$	$\mathit{m}=\mathit{M}-1$
$k=0$	$1$	$1$	$\cdots$	$1$	$k=0$	$1$	$-\frac{1}{M-1}$	$\cdots$	$-\frac{1}{M-1}$
$k=1$	$X_{ij}^{(1,0)}$	$X_{ij}^{(1,0)}$	$\cdots$	$X_{i,j}^{(1,0)}$	$k=1$	$0$	$0$	$\cdots$	$0$
$k=2$	$X_{i,j}^{(2,0)}$	$X_{i,j}^{(2,0)}$	$\cdots$	$X_{i,j}^{(2,0)}$	$k=2$	$0$	$0$	$\cdots$	$0$
$⋮$	$⋮$	$\ddots$	$⋮$		$⋮$	$⋮$	$\ddots$	$⋮$