3 × 2 complex matrices
No component greater than 1 in absolute value
A 3×2 matrix has a zero singular value if and only if one column is a multiple of the other.
[ 1 1+1j; -1j 1-1j; -1 -1-1j] 3 0 [-1 -1+1j; 1j 1+1j; 1j 1+1j] 3 0 [-1+1j -1j; -1+1j -1j; -1+1j -1j] 3 0 [-1 -1+1j; -1j -1-1j; -1j -1-1j] 3 0 [ 1 1-1j; -1j -1-1j; 1 1-1j] 3 0 [ -1j 1-1j; -1j 1-1j; -1 -1-1j] 3 0
These all, therefore, have two non-zero singular values and thus the columns are not scalar multiples of each other.
[-1 -1-1j; -1-1j -1-1j; -1-1j -1 ] 3 1 [ 1-1j 1 ; 1-1j 1-1j; 1 1-1j] 3 1 [ 1+1j 1+1j; 1 1-1j; 1-1j 1 ] 3 1 [-1-1j -1j; -1+1j -1-1j; 1j -1-1j] 3 1 [-1+1j 1j; -1j 1-1j; 1-1j 1-1j] 3 1 [ 1j 1j; -1j -1j; -1+1j 1-1j] 2 2 [ -1j -1-1j; 1+1j 1-1j; -1-1j 1j] 3 1 [ 1-1j -1j; 1+1j 1+1j; -1 -1-1j] 3 1 [ 1-1j 1+1j; 1 -1j; 1 -1j] 2 2 [ 1+1j 1-1j; 1 1j; 1j -1 ] 2 2 [ -1j -1-1j; 1+1j 1+1j; 1-1j 1 ] 3 1 [ 1-1j -1-1j; -1-1j 1j; -1j -1-1j] 3 1 [ 1 -1-1j; 1+1j 1-1j; 1-1j -1j] 3 1 [-1 1 ; 1 -1 ; -1-1j -1-1j] 2 2 [ 1-1j 1-1j; 1 -1 ; 1 -1 ] 2 2 [-1 1-1j; -1+1j -1-1j; -1-1j -1j] 3 1 [-1+1j 1+1j; 1j 1-1j; 1-1j -1j] 3 1 [ -1j 1+1j; -1+1j -1 ; -1+1j -1-1j] 3 1 [-1+1j 1j; 1-1j 1-1j; 1 1+1j] 3 1 [-1-1j -1j; 1-1j 1-1j; 1 1-1j] 3 1 [ -1j 1j; -1+1j -1+1j; -1 1 ] 2 2 [ 1j 1j; -1-1j 1+1j; 1 1 ] 2 2 [ -1j 1 ; -1+1j 1+1j; -1j 1 ] 2 2 [ -1j 1-1j; 1-1j 1j; 1+1j -1+1j] 3 1 [-1+1j -1 ; 1j -1-1j; -1+1j -1-1j] 3 1 [ 1+1j 1-1j; -1+1j 1j; -1j -1+1j] 3 1 [-1+1j 1+1j; 1j -1 ; 1j -1 ] 2 2 [-1-1j -1+1j; 1 -1-1j; 1+1j 1 ] 3 1 [-1+1j -1j; 1+1j -1-1j; -1 1+1j] 3 1 [ 1j -1 ; -1+1j 1+1j; 1j -1 ] 2 2 [-1 1 ; -1+1j -1+1j; -1 1 ] 2 2 [-1-1j 1j; -1+1j 1-1j; 1 -1+1j] 3 1 [ -1j 1+1j; -1-1j 1j; 1+1j -1-1j] 3 1 [ 1+1j -1+1j; -1+1j -1j; 1 1+1j] 3 1 [-1+1j 1+1j; -1j -1+1j; 1-1j -1j] 3 1 [ -1j 1-1j; -1+1j -1+1j; -1-1j -1 ] 3 1 [ 1+1j -1-1j; -1j -1+1j; -1+1j -1j] 3 1 [ 1j -1 ; 1j -1 ; 1-1j -1-1j] 2 2 [ -1j -1+1j; -1-1j 1+1j; -1-1j 1 ] 3 1 [-1+1j 1+1j; 1j 1+1j; 1+1j -1j] 3 1 [ 1+1j 1-1j; -1-1j -1 ; -1j -1+1j] 3 1 [ 1-1j -1 ; 1j 1+1j; 1+1j 1-1j] 3 1 [ 1+1j 1j; 1+1j 1+1j; 1j 1+1j] 3 1 [-1+1j -1 ; -1-1j -1-1j; -1j -1-1j] 3 1 [-1+1j -1+1j; -1-1j -1 ; -1j 1-1j] 3 1 [ 1j -1-1j; -1+1j -1 ; -1+1j -1-1j] 3 1 [ 1+1j 1+1j; 1 1+1j; 1+1j 1 ] 3 1 [-1 1-1j; 1+1j -1j; -1-1j 1+1j] 3 1 [ 1j 1-1j; 1-1j 1j; 1-1j -1+1j] 3 1 [ 1+1j 1+1j; -1 -1-1j; 1-1j -1j] 3 1 [ 1+1j -1-1j; -1-1j 1j; -1 1-1j] 3 1 [ 1 -1+1j; 1-1j -1 ; -1+1j 1-1j] 3 1 [-1 1-1j; 1+1j -1+1j; 1-1j 1 ] 3 1 [-1-1j -1j; -1 1-1j; 1-1j 1+1j] 3 1 [ 1-1j 1+1j; 1j 1 ; -1j -1 ] 2 2 [ 1-1j 1-1j; 1+1j 1j; -1 -1+1j] 3 1 [ 1 1+1j; 1-1j 1+1j; -1+1j -1j] 3 1 [-1 1j; -1+1j -1-1j; 1 -1j] 2 2 [ 1+1j -1-1j; 1 -1+1j; -1-1j 1j] 3 1 [-1 -1 ; -1-1j 1+1j; 1 1 ] 2 2 [ -1j 1-1j; 1-1j 1j; -1+1j -1-1j] 3 1 [ 1 1 ; -1-1j 1+1j; 1 1 ] 2 2 [-1+1j -1 ; 1 1-1j; -1+1j -1+1j] 3 1 [ 1j 1-1j; 1+1j 1-1j; 1-1j -1j] 3 1 [-1 -1+1j; 1-1j -1 ; 1+1j 1-1j] 3 1 [-1-1j 1-1j; -1-1j 1 ; 1j -1+1j] 3 1 [ 1-1j -1+1j; -1 1-1j; 1+1j -1j] 3 1 [ 1+1j 1+1j; 1-1j -1j; 1j -1+1j] 3 1 [-1 1+1j; -1-1j -1 ; 1+1j 1-1j] 3 1 [ 1j -1j; 1 -1 ; 1-1j 1-1j] 2 2 [ 1j 1j; -1-1j 1+1j; 1j 1j] 2 2 [-1+1j -1+1j; -1 -1-1j; -1-1j -1 ] 3 1 [ 1 -1-1j; 1+1j -1 ; 1-1j -1+1j] 3 1 [-1+1j -1-1j; -1j 1+1j; -1+1j -1 ] 3 1 [ 1+1j -1+1j; 1-1j 1j; 1 1+1j] 3 1 [ 1j -1-1j; -1-1j 1-1j; 1+1j 1j] 3 1 [ 1+1j 1+1j; 1j -1j; -1j 1j] 2 2 [-1 -1-1j; -1-1j -1-1j; -1-1j -1 ] 3 1 [-1-1j 1-1j; 1-1j 1j; 1j -1+1j] 3 1 [-1-1j -1 ; -1 1+1j; 1-1j -1-1j] 3 1 [ 1+1j 1 ; 1j 1-1j; -1-1j -1+1j] 3 1 [ 1+1j -1j; 1+1j 1-1j; -1 -1+1j] 3 1 [-1-1j -1+1j; 1 1j; -1j 1 ] 2 2 [-1 -1-1j; 1+1j -1+1j; 1+1j -1 ] 3 1 [-1+1j -1+1j; 1j -1j; 1 -1 ] 2 2 [ 1-1j -1j; -1-1j -1+1j; 1 -1-1j] 3 1 [ 1-1j 1-1j; 1 -1 ; 1 -1 ] 2 2 [ 1+1j -1 ; -1-1j 1+1j; -1 1+1j] 3 1 [ 1+1j 1 ; 1 1+1j; -1-1j -1-1j] 3 1 [-1+1j -1j; 1j 1-1j; 1+1j -1-1j] 3 1 [ -1j 1+1j; -1-1j 1-1j; 1-1j 1 ] 3 1 [ 1+1j -1j; 1+1j 1-1j; 1j 1+1j] 3 1 [ 1+1j 1 ; -1j -1+1j; 1+1j 1-1j] 3 1 [-1-1j -1+1j; -1 1+1j; -1-1j -1 ] 3 1
No component greater than 2 in absolute value
As these are randomly generated, only the first has the columns being scalar multiples of each other.
[ 2+1j -2-1j; -1+2j 1-2j; -2-2j 2+2j] 6 0 [-1 -1+2j; -1+2j 1j; 1+2j -2-2j] 4 3 [-2-2j -2+1j; 2j -1 ; -1-1j 1-2j] 4 3 [ -1j -2-1j; -2+2j 1 ; 1-2j 2-1j] 4 3 [-1+1j -1-1j; -1 -1+2j; 1-2j -1-2j] 4 2 [ 2+1j -1 ; -1j 1j; 1+2j -2 ] 4 1 [-2-1j 1 ; -2 -2+1j; 1-2j -1+2j] 4 3 [ 2+1j 2-1j; 1-1j -1-1j; -2-1j -1j] 4 2 [ 1 -2 ; -2 2-1j; 1 -1-1j] 4 1 [ -2j 2+1j; -2+1j 2+2j; -1+1j -1 ] 4 3 [ 2+2j -2 ; -2+1j -1 ; -1j -1 ] 4 2 [ 1j -2+2j; -2-2j 1+2j; 1-1j -1j] 4 3 [-1+2j 1 ; 2j -1+2j; 2-1j -1+2j] 4 3 [ -2j 2-1j; -1+2j -2j; 1-2j -1-1j] 4 3 [ -2j 1-2j; 1-1j -2-2j; 1-1j 2-2j] 5 2 [ 1 -1j; -1+2j 1-2j; 2-2j 1-2j] 4 3 [ 1+1j 2-1j; 1j 2-2j; 2+2j 1j] 4 3 [-2 -2-1j; -1+1j -1j; -2+2j 2-1j] 4 3 [-1-2j 2 ; 2j -1j; 2-2j 2j] 5 1 [ 1-2j -1-2j; 1 -2+2j; -1-2j -1j] 4 3 [-1 -1+2j; -1 1j; -2 -2+1j] 4 1 [ 2-2j 2+2j; -2+2j 2+2j; 2+1j 2j] 5 4 [ 2-2j 2+2j; 1-2j -2j; 2-2j -2-2j] 5 4 [ 2+2j -1-2j; -1+1j -1j; -2 -2-1j] 4 3 [ 2j -1-2j; -2-2j -1j; -1-1j -2-1j] 4 3 [ 2-2j -1-2j; -1j -1j; 2+1j -1+2j] 4 3 [ 2+2j 1 ; 1+2j -1-1j; 1j 2+2j] 4 3 [ 2-2j 2+1j; -2-1j -1+2j; 1 1 ] 4 3 [ 1+2j 2+2j; 1-2j -1+2j; 1 -1j] 4 3 [ 2+1j -2 ; 1j -2+2j; 1+2j 1-1j] 4 3 [ 2j -2j; 1-1j 2+2j; -1-2j -1-1j] 4 3 [ 1-2j 1-1j; -1+1j -2j; 2 -2-2j] 4 3 [ -2j -1j; -1-2j 2+2j; 2+1j 1-1j] 4 3 [ 1+2j -2-1j; 2+1j 2 ; 1j -2-1j] 4 3 [ 1+2j -1 ; 2j -1+2j; 1+2j 2-1j] 4 3 [-2 -1 ; 1+1j -1+2j; 1-2j -2+2j] 4 3 [ 1 -2-2j; -1-2j 1-1j; 2-2j -1 ] 4 3 [-2+1j -2 ; -2-2j 2+1j; -1j -1-1j] 4 3 [-1-2j 2 ; 1+1j -2-1j; -2 -1+2j] 4 3 [ 1-2j 1j; -2-2j -2+1j; -1j 2-1j] 4 3 [ 2-1j -2 ; -2-2j -1-2j; -1j 1-1j] 4 3 [ 1-2j 2-1j; 2j -1-2j; -1-2j -1 ] 4 3 [ 1+2j -2 ; 2-2j -2-1j; -1j 1-1j] 4 3 [ 2-2j 2-2j; 2 -2-1j; 1+2j 2j] 5 3 [ 1-2j 1 ; -2 1+2j; -1+2j -2-1j] 4 3 [-2+1j 2-1j; -2+2j -1 ; 1j -1+2j] 4 3 [ 2-2j 1 ; 1 -1+2j; 1-2j -2+1j] 4 3 [ 1 -1+1j; -2+2j 2-1j; 1+2j 2j] 4 3 [ 2j -2j; 2+2j -2+1j; -2-1j -2-2j] 5 3 [-2+2j 2-2j; -2+2j -1j; 2+2j 2+2j] 5 4 [-1-1j 2+1j; 2+2j 2-1j; 1 2j] 4 3 [ 2-1j -1-1j; -1 2-2j; 1-2j 2 ] 4 3 [ 2-1j 2j; 2-1j 2-1j; 1 -2-1j] 4 3 [ 2-1j 2-2j; 2 -2+1j; 1-1j 1 ] 4 3 [-2+2j 1-2j; -2j 2 ; 2-1j -2-2j] 5 3 [-1+2j 2-1j; -1j 2-2j; 2-1j 1j] 4 3 [ 2+2j 2+2j; 2-1j 2 ; 2+2j -2-2j] 5 4 [-2-2j 2+1j; -2 1j; 1-1j 2-1j] 4 3 [-2-1j 2+2j; -1-2j -1-1j; -2 -1 ] 4 3 [-1-2j -1 ; 2-1j 1+2j; -2 -1+2j] 4 3 [-2+1j -1j; -2j -2j; 1+2j -1 ] 4 2 [ 1-2j -1j; -2j 1+2j; -2-1j -2+1j] 4 3 [ 1 -2-1j; 2+2j -1j; 1-2j 1-2j] 4 3 [ -2j 2-1j; 1-2j 2j; -1+1j 1+2j] 4 3 [ 2+1j -1+1j; 1-1j 2-2j; -2j -2 ] 4 3 [ 1 -1+1j; -2-2j -2+1j; 1-2j 2 ] 4 3 [-1+2j 2j; 1-2j 1+2j; -1 -2+1j] 4 3 [ 1+2j 2 ; -2+2j 2-2j; 2 -1+2j] 5 3 [-2+2j -2j; -1-1j 1-1j; -1-1j -1+1j] 4 2 [-2 2 ; 1+1j 2-1j; 2+2j 1+1j] 4 3 [-2+2j -1 ; -1+2j 1-1j; -1j 2-2j] 4 3 [ 2-2j -2+1j; 2+1j 2 ; 1 1+1j] 4 3 [ 1 -2-2j; -1+1j 1 ; -2-2j -1-2j] 4 3 [ 1+2j 1+2j; -1 2+2j; -2+1j 1 ] 4 3 [ 2-2j -1-1j; 2j -2 ; 1-1j 1+2j] 4 3 [-2+1j -2j; 2j 2+1j; -1+2j -1-1j] 4 3 [ 2+2j 2-2j; -2-2j 2-2j; 2+2j -1 ] 5 4 [ -2j 2 ; 1-2j 2-2j; -2-2j -2+1j] 5 3 [-2-1j -2j; 2-2j -1-2j; 1 -1+1j] 4 3 [-2-1j 2-2j; 2 1-2j; 1+1j 1j] 4 3 [-2-1j 1+1j; -1 1-1j; -1+1j -2-2j] 4 2 [-1+2j -1+1j; 2 2 ; 1-1j -2+2j] 4 3 [ 2+2j -1+2j; -1j 2j; -1-1j -1+2j] 4 3 [ 2-2j -2+1j; 1-1j 1j; 2j -1+2j] 4 3 [-2-1j -2j; 2-2j -2+2j; 2+2j 2+2j] 5 4 [ 2-1j -1-1j; 1+1j 2+2j; 1j 1+1j] 4 2 [ 2+2j 2+2j; -2-2j -1+2j; 2-2j 2j] 5 4 [ 1+1j 2+2j; 2 -2 ; 1+2j 1+1j] 4 3 [ 2 2j; 1j 1-2j; -1 2+1j] 4 2 [ 1+1j 1 ; -1 -2+2j; 2-2j 1+2j] 4 3 [ 2j 1j; 2j 1-1j; -2 2+1j] 4 2 [-2+1j 1 ; -2+1j -2-1j; -2j -1+2j] 4 3 [-1-1j -2 ; -1-1j -2-2j; 2-1j -2-2j] 5 2 [ -2j -2j; 2j 2j; 2-2j -2+2j] 4 4 [ 1+2j -1 ; 2j 1+2j; 1+2j -2-1j] 4 3 [ 2 1 ; -1-2j -2+2j; 1-1j 2+1j] 4 3 [ 2-1j 2-1j; 1j 2-2j; 2-1j -1 ] 4 3 [ -1j 2-2j; -1-1j -2+1j; -2-2j 1j] 4 3 [ 1 -2+2j; -2+2j -2+2j; -2+2j 2-2j] 5 4 [ 1 -2-2j; 2+2j 1j; 2+2j 2-2j] 5 3
No component greater than 3 in absolute value
[ 2+3j -3-1j; -2j -1-3j; 1-1j -1-1j] 5 4 [ 2+1j -3-1j; -1-3j 1-3j; -3+1j 1+2j] 5 5 [ 3-1j 2+3j; 3-1j 2j; -3-3j 1+3j] 7 4 [ 1+1j -2+2j; 3-3j 2+2j; 2 2+3j] 7 2 [ 2-2j 1+2j; -1-3j 2+3j; 1j 2+2j] 6 3 [-2+2j -3+2j; 2-2j 1j; -3-1j -2+1j] 6 3 [-1-2j 2j; -2 -2-1j; -3+3j -3j] 6 3 [ 3j -1+1j; 2j 3+2j; -3+2j -2 ] 6 3 [ 3+2j 2-2j; -2j -2-1j; -1-1j 3+2j] 6 3 [-3-1j -3+2j; 3-3j -3-2j; 3-1j -3 ] 8 3 [ 3-1j 1+1j; -1-1j 3+2j; -1+3j 2j] 5 4 [-3+3j 3 ; 3-3j -2+2j; -3+3j -1-1j] 8 3 [ 1+3j -2 ; 2-1j -3+1j; -2-1j -3-3j] 6 4 [ 3 -1 ; -3 -2+3j; -3j -2j] 6 3 [-3+1j 1+1j; -1-3j 2-3j; -2-1j 1+3j] 5 5 [-2+3j -3+3j; -1-2j 2+2j; -2-2j 3j] 6 5 [ 2+3j 2-2j; -2 -2+1j; -1-1j -2-3j] 6 3 [ 1+2j 2-2j; -2 1-2j; -3-1j 3-2j] 6 3 [ 1-1j -3+2j; 1+3j -1+2j; 3-1j -1 ] 5 4 [-2-3j -1+1j; -2 1-1j; -1-1j 3-3j] 5 4 [ 2-3j -2+2j; 3 2-2j; -2+3j -3-1j] 6 5 [-3+3j 3-3j; 3-3j -3+3j; -2+2j 2+1j] 9 2 [ 2+2j 2 ; -2+2j -3-2j; -3 2+2j] 5 5 [ 2j 2-1j; 1-3j 2+1j; 2-2j -3j] 5 4 [ 1+1j 1-3j; 3+3j -3-3j; -1-3j -1+3j] 8 2 [ 3+1j 2j; 3+3j 3+2j; 1+3j -3+3j] 8 3 [-2-3j -3-3j; -3+2j 1+3j; -3j -3+1j] 8 3 [-3-3j 3 ; 2j -1+1j; 2j 2-2j] 6 3 [ 3+3j 1+3j; 1-1j -2j; -3+3j 3+2j] 7 4 [ 3+2j -1+1j; 1-3j 2-3j; 3-3j -3+3j] 7 5 [ -1j 3+2j; -3j -2-3j; 1 -2-2j] 6 3 [ 3j 1+1j; -2j 3j; -3-2j -2+2j] 6 3 [-3-2j 3-3j; -1+3j -2+3j; -1+3j 3+1j] 7 5 [ 2-2j -3-3j; 3j -1+3j; 1+1j -3+3j] 7 4 [-3+2j -2+2j; 3-2j -2+2j; 1j -3-3j] 6 5 [ 2-2j 1j; 2-1j 3 ; -2+3j 3j] 6 3 [-2 3+1j; 2j -2-2j; 3+3j -1j] 6 3 [ 2-1j -1+3j; -1+3j 2-1j; 1+1j 1+1j] 5 3 [ 2+2j 3j; -1+2j -2-3j; -2-3j -2+3j] 6 5 [-1-2j -3+1j; -3-1j 3-1j; -3-1j -2-1j] 5 5 [ 1+3j -1-3j; 1+2j -1+3j; 3+1j 2-1j] 5 5 [-2 -2j; -2+2j 3+1j; 3-1j 1+2j] 5 4 [-3-1j -3-1j; 3+1j 2 ; 3-3j 3-2j] 8 1 [ -1j 2+1j; -1+2j -2+3j; -2+3j 2 ] 5 4 [ -1j 2-2j; 2-2j -1 ; 3 -3+3j] 6 3 [ 2 -2+1j; -1-1j -2-3j; -2+3j -2-2j] 6 3 [ 1j -1-3j; -2-2j -2j; -1-3j -2+2j] 5 4 [ 3+3j -1 ; 3j -1+1j; 3+3j 3+1j] 7 3 [ 2+2j -2+3j; -3 -2j; -3+3j -3-2j] 8 1 [-3 3-3j; -3+2j 3-1j; 2+2j -3-1j] 8 2 [ 1-3j -1+2j; -2+1j -2 ; -2j -2-3j] 5 4 [-3-1j 3 ; -3 1+3j; -3-1j 3-1j] 7 3 [ -1j -3+3j; -2-3j -2-2j; -3+2j 2-2j] 6 5 [-1+1j -3-2j; 3+2j 2 ; -2 2-1j] 5 4 [ 3-2j -3 ; -3+3j 1-3j; 2+3j -2-1j] 8 2 [ 2+3j 3-3j; -2+3j -2-2j; 2+2j 1j] 6 5 [-3+2j 2j; -1+2j 2 ; -1j -3+3j] 6 3 [ 2j -3+1j; -3-3j 3-3j; 1+2j -3+1j] 8 1 [ 1-2j 3+3j; -3j -3-1j; -2+1j 3+3j] 7 4 [ 2-1j 1+1j; -3-1j -3+2j; -3-1j 3-1j] 5 5 [ 2-3j -3-3j; 1+3j -3-3j; 2 -1-1j] 7 4 [ 3+1j -3 ; 3+3j -3+2j; -3-1j -1+2j] 7 4 [ -1j 3-1j; 1-3j 3-3j; -3-3j -1j] 7 3 [ 3+2j -1j; 2j 2-1j; -1+2j -3+2j] 5 4 [-2+2j -2-1j; -2+3j 1+3j; 1+2j 2j] 6 3 [ 3-2j -2-2j; 2j -3-3j; 2+2j 1+3j] 6 5 [ 3+2j -3+1j; 3j -1-3j; -3+2j 1-3j] 8 1 [ 3j 2j; -2-3j 3+3j; -3-2j -2 ] 6 5 [ 1j -1+1j; -1+2j -1-3j; 2-3j -1-3j] 5 4 [ 2+1j 1-3j; -2+2j -1 ; 2+3j 2+2j] 6 3 [ 2+3j -2j; 3+3j 3j; 2 -3-2j] 6 5 [ 2+2j -1j; -1+3j -1+2j; 2-2j -2-3j] 6 3 [ 1 3j; -2j 1j; 3j 1j] 4 3 [ 2-3j 1 ; -2 -1+2j; 2-1j -2+3j] 5 4 [ 3+2j 2+2j; -1 3+1j; 1+2j 2+2j] 6 3 [ 1+3j 3j; -3 3-1j; -3-3j -3+3j] 7 5 [ 3+3j 2+1j; -3-3j -2-3j; 3+3j -1j] 8 3 [ -2j -1 ; 2j 1+2j; 3+3j -2+3j] 6 3 [ 3-3j 3-2j; 1+3j -2+3j; -1+3j 2j] 8 2 [-2 2+3j; 3+2j -1-2j; -3j 1 ] 6 3 [ 3+3j -3+2j; 2-2j 2+3j; -2 -3j] 8 1 [-3+2j -2j; -2-1j 3+1j; 2+2j 1-2j] 6 3 [ 1+1j -1+3j; 3-2j -3-1j; -2j 1-1j] 5 4 [-3-1j 2-1j; 1+3j 3-1j; -1-2j 1-3j] 5 5 [-1-3j 3+3j; -3-1j 1-1j; -3j 2j] 7 2 [ 3-1j 1+3j; 3-2j -3-3j; -3+1j -3+2j] 7 5 [ 1-3j 1-3j; 3+1j -1-2j; 1-1j 2j] 5 4 [-3+1j 3+3j; -2 3+3j; -2+1j -3+3j] 8 3 [-2+1j 1+3j; 1-3j 2 ; 1-2j 3+3j] 6 4 [ -1j 2 ; 1+3j 2-3j; -2-2j 3 ] 6 3 [-1-2j -1+2j; -3-2j -3+2j; -1-1j 1+1j] 6 2 [-1+3j -2+2j; -2j -2-3j; -1-3j -2-2j] 7 2 [ 2+2j 1 ; 3 3j; -3j -3j] 6 3 [-3-1j 3+2j; -2j -1-2j; 1+2j 2j] 5 4 [ 1-3j -3 ; 3-3j -2-1j; 3-3j -2+3j] 8 3 [ 1+3j 3+1j; 2-3j -3-3j; -2 -1+3j] 8 1 [-2-1j -2j; 2+1j -3 ; 3j 2-3j] 6 3 [ 3+1j 3+2j; 3+1j -2+3j; 3+3j 1 ] 7 4 [-2 -1-2j; -2 -1-2j; -3-3j -3 ] 6 3 [-2 -2+3j; 3-3j 2+1j; 3+2j -2-2j] 6 5
No component greater than 4 in absolute value
[-3-1j -1+2j; 4+4j -2-3j; 3j 2+4j] 8 5 [ 2 2+4j; -2-3j 2j; 2-4j -3-2j] 7 5 [-3+1j -4-3j; -4-2j -3 ; -4-4j 1+4j] 8 7 [-4-2j -1 ; 1j -4-1j; 1j -1 ] 5 4 [ -4j -4+4j; 1-3j -1+1j; -2j -2 ] 8 2 [-4 4-4j; -4+2j -2+4j; -2j 3-4j] 9 6 [-2+4j -1+2j; 2-3j 2-4j; -2-1j 1-3j] 8 3 [-4-2j -1-3j; -2-1j 4-4j; 2-3j -4-2j] 8 6 [ -3j 1j; 1 2+1j; -4+3j 4+4j] 8 3 [ 4-1j 4+4j; 3j 1 ; -3 -1-2j] 8 3 [ 1+1j 2-4j; -4-4j -1+2j; -3-1j -4j] 7 6 [-4 4 ; 4+1j -4+3j; 3+4j 1-4j] 10 4 [ 4-1j 1+4j; -4+4j 2+4j; -3+2j -1j] 8 6 [ 2j 1+4j; 1-4j -4+2j; -2-2j 2-2j] 7 5 [ 4j 2-4j; 2j -4+2j; -4j -3j] 7 6 [ 4+1j -1+2j; -1+2j 4 ; -2-3j -2-1j] 6 5 [ 3+1j 2+2j; -1-3j 4+4j; 4-4j 3-4j] 9 6 [ 4+3j -1+2j; -3-2j 3+4j; -2-3j -4-4j] 8 7 [ 4j -4+4j; 4-4j 1j; 4-2j -4j] 9 6 [-4+1j -1-4j; -4+4j 1j; -2-1j -4-1j] 8 5 [-2+4j -4j; 4 4-2j; -2+3j -4+4j] 9 6 [ 1+2j -4+2j; 1-2j -3j; -3-4j -3+4j] 8 5 [-3-1j -4-1j; -2-1j -4-2j; 4-2j -1+4j] 8 5 [-2+1j 4 ; 4j -1 ; -4+2j -4 ] 7 5 [-2+2j -4+4j; 4+4j -1+1j; -4j -3+1j] 8 6 [ 2j 4+4j; 4+2j -4 ; 4+2j 2-2j] 8 6 [ -4j -2-1j; -4-1j -4+2j; 2-1j 3+1j] 8 3 [-1 3+1j; 1j 4-4j; -4-2j 1j] 7 4 [ 4+3j 1+1j; 2 -4+1j; 2-1j -2-2j] 6 5 [-2-1j -4+4j; -3-4j 1-4j; -2-1j -1+2j] 8 5 [ -4j -2-1j; -2-3j 1-2j; -3 -1-4j] 7 4 [-4+4j 3+4j; 4-4j -1 ; 1+3j 3 ] 10 3 [ 1+2j 4-3j; 2+3j 2-1j; -4-2j -2+1j] 8 3 [-4+4j -2+4j; -2-4j 2-1j; 4j -2 ] 9 4 [ 1+3j 3+1j; -2-4j 4+2j; 4-4j 2-2j] 8 6 [ 1 2j; 2+4j 4+3j; -4 2-2j] 7 5 [-4-2j 1j; -1 1-1j; -1+4j 4-4j] 8 3 [ 2+4j 3-3j; -2+4j -2-4j; 2j -3+3j] 8 6 [-2 3-4j; 1+4j 3+1j; 4+1j 4 ] 8 5 [-4-2j 1-2j; -4 3-2j; -1-1j 4-1j] 8 3 [ 3j 4j; 1-1j 1 ; 4 -4-1j] 6 5 [ 2-1j 2+2j; 4+1j -4+2j; 2+2j -3-1j] 8 2 [-2+2j 4+1j; -4-2j 1+4j; -1-3j -1j] 8 3 [ 2j -4+2j; 4+2j -2-4j; -2+4j 4j] 8 6 [ 4-4j -2 ; 3-3j -4j; 1 3+3j] 8 5 [-4-2j 3 ; -4-1j -1-1j; 3+4j 4 ] 8 5 [-4-4j 1-2j; 1-1j -3 ; 4+3j -4j] 8 5 [ 4+4j -4j; 4+1j -2-2j; 4j -2-4j] 10 3 [-4 -1+3j; 4 3-1j; -4-4j 4 ] 8 6 [ 1-1j 3j; 4-2j 1+2j; 1-2j -4-2j] 6 5 [-4-2j 2+2j; 4 3 ; -2-1j -4 ] 7 5 [ 1-1j 1j; -2j 4+1j; -4-2j 1 ] 6 3 [-1 -3-4j; -4j -1j; -4+1j 1 ] 6 5 [-1-2j -1-3j; 4-4j -1-4j; -3+2j -4+4j] 10 3 [ 4+4j 1j; -1j -4 ; 1+1j -3j] 6 5 [ 1-1j 3+2j; -2j 1+1j; -4+4j -4+2j] 8 3 [ 4 -4-3j; 1-4j -2-2j; -3-3j 2-1j] 8 5 [ 3+1j -1+1j; 4j 4+4j; -4+2j 4-2j] 8 6 [-2-4j -2-4j; -4+4j -2j; 2 -4+2j] 8 6 [ 1-2j 1j; -2-3j -4-1j; -4-1j -4-2j] 8 3 [ 4-4j -2j; -2j -2+4j; 2-4j 2+4j] 8 6 [-4 2-4j; 4+2j -4-3j; -2-4j -4 ] 9 6 [ 3-4j -1-4j; 1j 1 ; -2+2j -1 ] 7 2 [-4-1j 2+4j; -4j -2-1j; 1+2j -1-3j] 8 3 [-4-4j -2j; 4 4-4j; -1-4j 4 ] 9 6 [ 2-4j 4+2j; 3-3j -3+3j; -4-4j 2-2j] 10 4 [ 3+4j -4+4j; -2-4j -4 ; -4-2j -2 ] 9 6 [ 1+3j -2+4j; -4 -4+3j; -4+2j -4-3j] 10 4 [ 2-4j -3+2j; 4+4j 2+1j; 1+1j 4-1j] 8 5 [-4-2j 3+3j; -3+1j -4-3j; 2-4j 4+4j] 10 5 [ 4-4j -3 ; 2+3j 1 ; 1+4j -1+4j] 8 5 [ 3-3j 1+2j; 2-4j -2-1j; -4j 3-4j] 8 5 [-4-3j 4+3j; -1 3+2j; -2-4j -4j] 8 6 [-4-4j -3+2j; 2+4j -4+1j; -1+3j -2-2j] 8 6 [-4+4j -1-1j; 4-4j -3+3j; 3-2j 4-2j] 9 6 [-2-2j -2-2j; 2+2j -2-2j; -4 -4+1j] 7 4 [ 1+3j 4-3j; 4+2j 4+4j; 2-4j -3-3j] 10 5 [-4-1j -1-3j; 2+4j -1-2j; -1-4j -2+4j] 8 5 [ 1+3j 2j; 4 4+4j; 1j 3-1j] 8 3 [-1-4j -3+3j; 1-3j -2+4j; -1-2j -1-3j] 8 4 [-2 -2+1j; -4+4j -4+1j; -1-1j -2-2j] 8 2 [-1-3j 1-2j; 1+4j 4-4j; -4+4j -4-1j] 8 7 [ 2 -3+4j; -4-2j 4+4j; 1-2j -2 ] 9 3 [-2-2j -4j; -4 -1+3j; 4+4j -3-3j] 8 6 [ 4-1j -4-4j; 2+1j 1-1j; 4j -1j] 8 3 [ 2-4j 3-4j; 4+3j 3-4j; -2+1j 4+3j] 10 5 [ 1+2j 1-4j; 3+2j -2+1j; -2+4j -2-1j] 7 4 [-2+4j 1-4j; -2+1j -2-4j; -1-3j -4+1j] 8 5 [-4-3j 2 ; -4+4j 4j; -2+4j -4-2j] 9 6 [ 1+1j -4+2j; 1+3j 4 ; 4+4j -2+1j] 7 6 [-4-4j -4+3j; -4-1j 4j; -1-3j 4+3j] 10 5 [-1-3j -1+1j; 1-3j -1+4j; -1-4j -3-3j] 7 5 [-4+3j 4+2j; 4-4j 1-4j; 3-3j -3+2j] 10 5 [ 4-1j 2+4j; -3+1j -2+1j; 4+4j -1-2j] 8 5 [-4 4-4j; 2-2j -4-3j; -4+2j 4j] 9 6 [-2-1j 1-4j; -2+2j -1+4j; 1+4j 3-4j] 8 5 [-1-1j -3-1j; 4-2j 4-1j; 1+1j -1+1j] 7 2 [-3-2j -3+3j; 1+2j 2+2j; -4+2j 4-3j] 8 5 [ 3j -4j; 3-1j -1 ; -4j -3j] 6 5 [ 3+1j -4+2j; 4 -4j; 3+3j -2+4j] 8 6
No component greater than 5 in absolute value
[ 5+1j -5j; 1+3j 5+5j; -4+3j 3-5j] 11 7 [-2-2j 1+1j; -2 5+5j; -5+3j -1+1j] 8 6 [ 1-4j -5-4j; -5+1j -1-3j; -3-4j -1-4j] 10 6 [-2+4j -5-2j; 5+2j 3+4j; -1j 1+2j] 10 3 [ 3-1j -1-5j; 4-2j 5+4j; 5-1j 3-5j] 11 6 [-2+3j -5+5j; -2-2j 5+3j; -5+4j -3-5j] 12 6 [ 1-3j -1-3j; 5+5j -2-2j; -5+5j 5+4j] 12 5 [-5+2j 5-1j; 2+1j -4-4j; 4+4j 1 ] 10 5 [ 5-5j -1-5j; 3+1j -5j; 4+5j -5+5j] 11 9 [ 5j -3 ; 3j 5j; -4+1j 2j] 8 5 [ 5+1j 2+4j; -1-1j -4 ; 1-1j 5-5j] 10 4 [-1+1j 5+4j; -1-3j 2+2j; 5-5j 1-1j] 8 7 [-3-1j -5-1j; -3+4j -4-2j; 5-1j -3+1j] 9 6 [-2+5j 3-3j; -1+4j 1+5j; 2-3j 3+1j] 8 7 [-5-1j -1+4j; 1-5j 5+2j; -1-1j -2-3j] 8 7 [ 1-2j -5j; 5j -5+4j; -1-3j -3-1j] 10 4 [-5+4j 1+2j; -2+4j 5 ; -3-2j -2+1j] 10 3 [-2-5j 1-3j; -4+3j -3-5j; -2-5j 5-1j] 12 3 [-5+1j 4-4j; -4j 4+3j; 4+2j -5-2j] 12 2 [-2-4j 1 ; 1-3j 5-5j; -5+1j 5-5j] 11 6 [ 4j -3+5j; -4-5j -3-1j; 2+3j -5-5j] 10 8 [ 3+3j -4+1j; -3-5j -3+2j; -1-1j 2-5j] 8 7 [ 3j -2-4j; -4 4+5j; 5-5j 3+2j] 10 7 [-5+5j 5-1j; 3-2j 5+1j; 1+5j -5-2j] 11 7 [ 5-5j -5-5j; -5+2j -2-2j; -3-3j -5+5j] 13 6 [-5+3j -2-4j; 3+1j -5+3j; 1+1j -4j] 10 4 [ -2j -5 ; 2-4j -3j; -1+5j 4-5j] 10 5 [-2+2j 5j; -1+3j 2-2j; -1+5j -2-2j] 7 6 [ 2-2j -1+1j; 4j -4 ; 1+5j -4-5j] 10 3 [-3+1j 3+1j; 5+5j 1-5j; -3-5j 3-5j] 10 8 [-4-5j 5+2j; 5-2j 4 ; -2-1j 2+5j] 10 7 [-1+4j -2 ; 4-4j -4-5j; 1+5j 1+2j] 10 5 [ 1-5j -3+5j; 3 4+2j; -1-5j -1+1j] 9 6 [ 4 2+5j; 4j 2+3j; -3+5j 1+4j] 10 5 [-2+5j 1+4j; 4+4j -4-3j; 2+1j 4-5j] 10 7 [ 5+1j -5-5j; 1j 1j; 3j 4-1j] 10 2 [ 2+5j 4+5j; -5-4j 2-4j; -2-3j -3-4j] 12 5 [-5-4j -5+3j; -3-1j 4-5j; 1-3j 3-5j] 11 7 [-3-1j -5-1j; -1+5j 1+2j; 5-2j 1+3j] 9 5 [ 1+5j 3+5j; 4 2-4j; -2j 4 ] 10 4 [-3-1j -5-1j; -3-4j -4+2j; 5-1j -3+1j] 9 6 [-1+2j 2 ; 4-1j 1-5j; -2-5j 2+2j] 8 5 [ 4j 5-3j; -1j -3+1j; 5+2j -1+3j] 8 6 [ 5-5j -1-5j; -3-4j 4+2j; -5-1j -1+3j] 11 6 [-3+5j 4 ; -4+2j 5j; -5+3j -4-2j] 10 7 [ 2+2j -1+4j; 5-2j -5+4j; -2-3j 1-4j] 10 5 [-3+2j -5-5j; 4j 5+3j; -5+4j -5+1j] 12 6 [-3-2j 4j; 5+3j 1+5j; 3+5j 5+3j] 11 6 [ 5-3j 5+4j; 4+2j -2-1j; -1-2j -2-4j] 10 5 [-1+3j -1+4j; -5-1j 4+5j; 5-5j -4-3j] 12 5 [ 2+4j -2-5j; 4-5j 2+4j; -3-2j -5-1j] 10 7 [ 3-5j 3+2j; -1+5j 5-4j; -5+5j -4j] 12 6 [-5-2j -2-4j; 4-1j -5-1j; 1-2j -4 ] 8 7 [-3+5j 1+5j; 2j -3-4j; -1-1j 5-1j] 9 6 [ -1j -5-1j; 5-3j 4 ; -4 4+2j] 8 7 [ 5-5j -2+1j; 2j -1-2j; -2+2j -4+5j] 8 7 [-3 -5-4j; 4-2j 1 ; -5+4j -4-3j] 11 4 [ 5+5j 4-2j; 1+5j 2+3j; -3+1j 5+5j] 12 5 [-5+3j -4 ; 4+5j 5-3j; 5j -5-5j] 10 10 [ 5+5j 1-5j; -1-4j 3j; -1j 1 ] 10 2 [ 2 -2+5j; 4+1j 5-5j; 5-2j -2+4j] 10 7 [ -1j 1-3j; -5-3j 1 ; 1+5j 5-3j] 9 5 [ 2+1j 3+2j; 3-5j 1+1j; -1+2j 4+5j] 8 6 [-1-3j 2+5j; 5-3j -2-2j; -1-5j 3j] 10 4 [ 1+2j -5j; 1j -2+3j; 2-5j -4j] 8 5 [-1+1j -2-1j; -5-5j -5-1j; -3-2j 3-1j] 9 5 [-4 5+5j; -3+4j 5+3j; -5+5j -5-5j] 12 9 [ 4-5j -5+2j; 1-2j 3-2j; 5-2j 4-4j] 10 7 [ 1-1j -5-1j; -2+1j 2+2j; 5-3j -5-5j] 11 2 [-5+3j 5+5j; -5+1j -2+2j; -1+5j 5j] 12 5 [ 2-1j 5-2j; 5+2j 4+2j; -5-4j 5 ] 10 7 [ 5+5j 2-5j; 3-1j 4+2j; -5+3j 5-5j] 12 7 [-1+3j -3-5j; -4-2j 1+3j; 2+5j 1+3j] 8 7 [-2-2j -5-4j; 5+5j -1j; 5-4j -2+2j] 10 7 [-1-5j 1-2j; -2-2j 5-2j; -5 2+4j] 8 7 [-1-4j 3+5j; -5j -3-3j; 3j -1+3j] 8 7 [-2 1-1j; 3-5j 1-1j; -3+2j 3+5j] 8 5 [-3-1j 1+5j; -3+5j -5-1j; 4+1j 2j] 9 6 [ 1+3j -5+1j; -5-1j -1+3j; 4-3j 4-2j] 9 6 [ 4+5j -4j; 1-3j 4+5j; -2-2j 3j] 10 5 [ 1-2j -2-1j; -5-5j -5+5j; 4-1j -1-4j] 12 0 [-3-1j 5+1j; 1-5j -3-5j; -4-2j 4+5j] 11 6 [-2+1j -1-1j; -2+4j 3-5j; -3+5j -3+3j] 8 7 [ 1+4j -2-5j; -5j 4-5j; 4+1j 4-2j] 10 7 [-1+2j -2-5j; 5j 2-1j; -1+2j 4+2j] 8 5 [-3+3j 1+1j; -5-1j -1-5j; 1-1j -5-1j] 8 6 [-5-3j 3-5j; -2-5j 2+2j; -1+1j -1-1j] 10 3 [ 2-4j -5j; -5+2j -4-4j; -3+5j 5-4j] 10 9 [ 3+3j 1+4j; -5+1j 5+2j; 1+3j -3+2j] 8 7 [-2+2j -1-3j; -1-5j 1+3j; 5j 3+5j] 8 7 [ 3-3j -3+1j; 3+3j -1+5j; 1+5j 1-1j] 8 6 [-5-1j 5+2j; 2+4j 2+1j; -1+2j -2 ] 8 5 [-1+2j 4+2j; -3-4j 2-4j; -5-2j -5-1j] 10 5 [ -1j -1+5j; -5-2j -4-4j; 2+5j 4-4j] 10 7 [-1+5j 2+5j; 4-2j 1-4j; -5-2j 2 ] 10 5 [ 2+5j -5-1j; -2 3-5j; 5-1j -5+3j] 12 3 [-5-4j 4 ; -3+1j 5-2j; 2-2j 1+2j] 10 3 [-5-1j 2-4j; 5-3j 1+2j; -3-5j 5-2j] 12 2 [-1+3j -1+3j; -1+5j 2-5j; 5+2j -1-1j] 9 5 [ 1+3j 1-5j; 5+1j 1 ; -4-1j 5-1j] 9 5
Douglas Wilhelm Harder
Department of Electrical and Computer Engineering
University of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
Phone: +1 519 888 4567 extension 37023
Fax: +1 519 746 3077
Department of Electrical and Computer Engineering
University of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
Phone: +1 519 888 4567 extension 37023
Fax: +1 519 746 3077
Website maintained by Douglas Wilhelm Harder