Hermitian 4 × 4 singular matrices
No component greater than 1 in absolute value
1 -1 -1 -1j; -1 1 1 1j; -1 1 1 1j; 1j -1j -1j 1] 4 0 0 0 1 1 1 1j; 1 1 1+1j 1j; 1 1-1j 1 1 ; -1j -1j 1 1] 4 1 -1 0 -1 1j -1-1j -1-1j; -1j -1 -1-1j 1+1j; -1+1j -1+1j -1 -1j; -1+1j 1-1j 1j -1] -4 -2 2 0 1 -1+1j -1j -1 ; -1-1j 1 1j 1j; 1j -1j 1 -1j; -1 -1j 1j 1] 4 1 -1 0 -1 -1 -1 -1+1j; -1 -1 -1j -1 ; -1 1j -1 1j; -1-1j -1 -1j -1] -4 1 -1 0 1 -1j -1j 1j; 1j 1 1+1j -1j; 1j 1-1j 1 -1 ; -1j 1j -1 1] 4 1 -1 0 1 -1j 1j -1j; 1j 1 -1+1j 1 ; -1j -1-1j 1 -1j; 1j 1 1j 1] 4 -1 1 0 -1 -1-1j -1j 1 ; -1+1j -1 -1j -1j; 1j 1j -1 -1 ; 1 1j -1 -1] -4 -1 1 0 1 -1 -1 1 ; -1 1 1j -1-1j; -1 -1j 1 -1 ; 1 -1+1j -1 1] 4 -1 1 0 -1 -1-1j -1 -1j; -1+1j -1 1j -1j; -1 -1j -1 -1j; 1j 1j 1j -1] -4 -1 1 0 1 -1+1j 1j 1j; -1-1j 1 1 -1j; -1j 1 1 -1j; -1j 1j 1j 1] 4 1 -1 0 1 1 -1j -1j; 1 1 -1-1j -1j; 1j -1+1j 1 1j; 1j 1j -1j 1] 4 1 -1 0 -1 -1-1j 1-1j 1 ; -1+1j -1 -1 -1-1j; 1+1j -1 -1 1-1j; 1 -1+1j 1+1j -1] -4 -2 2 0 -1 1j 1-1j -1+1j; -1j -1 1+1j -1-1j; 1+1j 1-1j 1 1 ; -1-1j -1+1j 1 1] -4 2 2 0 1 -1j 1 1 ; 1j 1 -1 -1+1j; 1 -1 1 1 ; 1 -1-1j 1 1] 4 -1 1 0 1 -1j -1 1+1j; 1j 1 1 -1 ; -1 1 1 -1 ; 1-1j -1 -1 1] 4 -1 1 0 -1 -1 1 -1j; -1 -1 -1j -1j; 1 1j -1 -1+1j; 1j 1j -1-1j -1] -4 1 -1 0 -1 1 1-1j 1+1j; 1 -1 1-1j 1+1j; 1+1j 1+1j 1 1j; 1-1j 1-1j -1j 1] 4 -2 -2 0 1 -1j 1 -1j; 1j 1 -1+1j 1j; 1 -1-1j 1 -1j; 1j -1j 1j 1] 4 1 -1 0 1 1 1+1j 1+1j; 1 1 1-1j -1+1j; 1-1j 1+1j 1 1j; 1-1j -1-1j -1j 1] 4 -2 2 0 1 -1 -1-1j -1+1j; -1 1 -1-1j -1+1j; -1+1j -1+1j 1 -1j; -1-1j -1-1j 1j 1] 4 -2 2 0 -1 -1j 1+1j 1-1j; 1j -1 -1+1j 1+1j; 1-1j -1-1j 1 -1j; 1+1j 1-1j 1j 1] 4 -2 -2 0 -1 -1j -1-1j 1-1j; 1j -1 -1-1j -1+1j; -1+1j -1+1j -1 -1 ; 1+1j -1-1j -1 -1] -4 -2 2 0 -1 -1 -1 -1 ; -1 -1 -1 -1-1j; -1 -1 -1 -1j; -1 -1+1j 1j -1] -4 1 -1 0 -1 -1+1j 1 1j; -1-1j -1 1 -1 ; 1 1 -1 -1j; -1j -1 1j -1] -4 -1 1 0 -1 -1 1+1j 1+1j; -1 -1 -1-1j -1-1j; 1-1j -1+1j 1 1 ; 1-1j -1+1j 1 1] 4 -2 -2 0 -1 1 1+1j -1-1j; 1 -1 1+1j -1-1j; 1-1j 1-1j -1 1 ; -1+1j -1+1j 1 -1] -4 -2 2 0 -1 1-1j -1+1j 1j; 1+1j -1 -1 1-1j; -1-1j -1 -1 -1+1j; -1j 1+1j -1-1j -1] -4 -2 2 0 -1 -1 1 1 ; -1 -1 1 1j; 1 1 -1 -1-1j; 1 -1j -1+1j -1] -4 1 -1 0 -1 -1 -1+1j -1+1j; -1 -1 1-1j 1-1j; -1-1j 1+1j 1 1 ; -1-1j 1+1j 1 1] 4 -2 -2 0 -1 1-1j 1j -1j; 1+1j -1 1 1j; -1j 1 -1 1 ; 1j -1j 1 -1] -4 -1 1 0 1 -1 -1j -1 ; -1 1 1j 1j; 1j -1j 1 1-1j; -1 -1j 1+1j 1] 4 -1 1 0 -1 -1 1-1j -1 ; -1 -1 -1j -1 ; 1+1j 1j -1 1 ; -1 -1 1 -1] -4 -1 1 0 1 -1-1j -1 -1+1j; -1+1j 1 1-1j 1j; -1 1+1j 1 1-1j; -1-1j -1j 1+1j 1] 4 -2 2 0 -1 -1 -1j 1j; -1 -1 -1j -1+1j; 1j 1j -1 1j; -1j -1-1j -1j -1] -4 -1 1 0 1 1j -1j -1j; -1j 1 -1-1j -1j; 1j -1+1j 1 1 ; 1j 1j 1 1] 4 1 -1 0 1 -1j 1j 1+1j; 1j 1 1j 1j; -1j -1j 1 1 ; 1-1j -1j 1 1] 4 1 -1 0 -1 -1-1j 1 -1 ; -1+1j -1 -1j -1 ; 1 1j -1 1j; -1 -1 -1j -1] -4 -1 1 0 -1 1j 1+1j 1j; -1j -1 -1 -1j; 1-1j -1 -1 -1j; -1j 1j 1j -1] -4 1 -1 0 1 -1 1-1j -1 ; -1 1 1j -1j; 1+1j -1j 1 -1 ; -1 1j -1 1] 4 1 -1 0 -1 1j 1 -1j; -1j -1 1 1-1j; 1 1 -1 1j; 1j 1+1j -1j -1] -4 1 -1 0
No component greater than 2 in absolute value
[ 1 1-1j 1+1j 2+2j; 1+1j 1 1j 1+1j; 1-1j -1j 1 1-1j; 2-2j 1-1j 1+1j -2] 5 -4 0 0 [-1 -2j -2 1+2j; 2j -1 -1-1j -2+2j; -2 -1+1j 2 -2j; 1-2j -2-2j 2j -1] 6 -4 -3 0 [ 2 2-1j 2 2+2j; 2+1j -2 -2+2j -2j; 2 -2-2j 1 -1j; 2-2j 2j 1j 1] -6 5 3 0 [ 1 -1j -1 -1-2j; 1j 1 1j 1 ; -1 -1j 1 -1j; -1+2j 1 1j 1] 4 -2 2 0 [-2 1-2j 2j -2-1j; 1+2j -2 1+2j -1+1j; -2j 1-2j 1 1+1j; -2+1j -1-1j 1-1j -1] -6 4 -2 0 [-1 1 -1-2j 2+1j; 1 2 1j 1-1j; -1+2j -1j -1 2+1j; 2-1j 1+1j 2-1j 1] -5 4 2 0 [ 2 1j -1+1j -1 ; -1j -1 1 1+2j; -1-1j 1 1 -1j; -1 1-2j 1j 1] 4 -3 2 0 [ 1 1-2j -2 -2 ; 1+2j 1 -2+2j -2 ; -2 -2-2j -1 -2-2j; -2 -2 -2+2j 1] -6 5 3 0 [-1 -2j 1 1-1j; 2j -2 1+1j 1 ; 1 1-1j -1 2j; 1+1j 1 -2j -2] -5 -3 2 0 [ 2 -1+1j 1+2j 1-2j; -1-1j -2 -1j -2-1j; 1-2j 1j -1 -2-1j; 1+2j -2+1j -2+1j 1] 6 -4 -2 0 [ 1 1+2j 2 1+2j; 1-2j 2 -2j -1j; 2 2j 2 -2 ; 1-2j 1j -2 -1] 6 -4 2 0 [-1 -1j -1+2j -1j; 1j -1 1 1 ; -1-2j 1 -1 1j; 1j 1 -1j -1] -4 -2 2 0 [ 2 -2-2j -2-2j -2 ; -2+2j -1 2+1j -1j; -2+2j 2-1j -1 -1 ; -2 1j -1 -1] 6 -4 -3 0 [ 2 -1 1 -1-1j; -1 -1 1+2j 2-1j; 1 1-2j -2 -1+1j; -1+1j 2+1j -1-1j 1] -5 4 1 0 [ 2 -2 -1+1j -2-2j; -2 2 -1-1j 2 ; -1-1j -1+1j 2 -1+1j; -2+2j 2 -1-1j 1] 7 2 -2 0 [ 2 -1-2j -2j 2j; -1+2j 2 1+1j -1 ; 2j 1-1j 2 2 ; -2j -1 2 2] 6 4 -2 0 [-1 -2+2j 2j -2+2j; -2-2j -2 -2 -2j; -2j -2 -2 -2j; -2-2j 2j 2j -2] -8 3 -2 0 [-1 -1+1j -2 -1+1j; -1-1j 2 -2+1j -2+2j; -2 -2-1j -1 1+2j; -1-1j -2-2j 1-2j 2] 6 -5 1 0 [-1 1 -1j 1j; 1 1 2 1-1j; 1j 2 -1 1+1j; -1j 1+1j 1-1j -1] -4 3 -1 0 [ 1 -2-2j -1+1j -1j; -2+2j 1 1-1j -1-2j; -1-1j 1+1j 2 -2j; 1j -1+2j 2j 2] 6 -3 3 0 [ 2 -2j 1+2j -1j; 2j 2 1-2j -1j; 1-2j 1+2j 1 2j; 1j 1j -2j -1] 5 -4 3 0 [ 1 -2 -1+1j -1+2j; -2 -2 1+1j -1+2j; -1-1j 1-1j 2 -2-1j; -1-2j -1-2j -2+1j -1] -6 4 2 0 [ 1 -2j 2 2j; 2j -2 1+1j -1-1j; 2 1-1j -1 1 ; -2j -1+1j 1 -1] -4 4 -3 0 [ 2 1-1j -1+2j 1j; 1+1j -2 1-2j -1 ; -1-2j 1+2j -1 1+1j; -1j -1 1-1j 1] -5 4 1 0 [-1 -1+1j -1 -2j; -1-1j -1 1j -1j; -1 -1j -1 -1 ; 2j 1j -1 -1] -4 -2 2 0 [ 2 -2j 1j 2-2j; 2j -2 2j -2j; -1j -2j -2 2 ; 2+2j 2j 2 -2] -7 4 -1 0 [-1 1 1 1j; 1 1 1j 1-2j; 1 -1j 2 1-1j; -1j 1+2j 1+1j 1] 4 -3 2 0 [-2 1+1j 1j 1-2j; 1-1j -1 1+1j 1 ; -1j 1-1j -2 -1j; 1+2j 1 1j 1] -4 -3 3 0 [ 1 -2 1-2j -1-1j; -2 2 1+1j -2-2j; 1+2j 1-1j 1 2+1j; -1+1j -2+2j 2-1j -1] -5 5 3 0 [ 1 1-2j 2-1j 1j; 1+2j 1 -1-1j 1+1j; 2+1j -1+1j 1 2-2j; -1j 1-1j 2+2j -1] -5 4 3 0 [ 1 2j 2j -2j; -2j -1 2j 1-1j; -2j -2j 1 2+2j; 2j 1+1j 2-2j 2] -5 5 3 0
No component greater than 3 in absolute value
[-1 1+2j 2+3j -2-1j; 1-2j -3 -1-2j 2+2j; 2-3j -1+2j 3 1+1j; -2+1j 2-2j 1-1j -3] -8 6 -2 0 [-1 3+2j 1-1j 1+1j; 3-2j -1 -2-3j -3+2j; 1+1j -2+3j 3 -2 ; 1-1j -3-2j -2 -3] -8 7 -1 0 [-1 -1+2j -3 -3+1j; -1-2j -1 -1+2j 2+3j; -3 -1-2j 3 3-2j; -3-1j 2-3j 3+2j 2] 10 -4 -3 0 [ 2 1j 1-2j -1-1j; -1j 1 1 1j; 1+2j 1 -2 1+3j; -1+1j -1j 1-3j 1] -5 4 3 0 [-1 1 -2-1j -1-3j; 1 2 -2+2j -1 ; -2+1j -2-2j 3 -1+2j; -1+3j -1 -1-2j -1] 7 -5 1 0 [-2 -2 2j 2j; -2 1 3-2j -1+3j; -2j 3+2j -2 -1-2j; -2j -1-3j -1+2j -3] -8 5 -3 0 [ 1 -2j -2 2+2j; 2j -3 3j -1j; -2 -3j -3 1 ; 2-2j 1j 1 -3] -8 3 -3 0 [ 1 -1-2j -1 -1 ; -1+2j 3 -3j -3j; -1 3j 2 1+1j; -1 3j 1-1j 1] 8 -2 1 0 [-1 -2-1j -1-1j 1 ; -2+1j -2 -2+2j 3 ; -1+1j -2-2j -2 1+1j; 1 3 1-1j -3] -8 -2 2 0 [-3 2j 2 2j; -2j -3 -2j 1+3j; 2 2j -3 -3j; -2j 1-3j 3j -1] -8 -5 3 0 [-3 2j -2+2j 3-2j; -2j 1 1-3j 2j; -2-2j 1+3j 2 2+2j; 3+2j -2j 2-2j 1] -8 6 3 0 [ 2 -2+2j 1+3j 2+2j; -2-2j 1 1-3j 2-3j; 1-3j 1+3j -1 -1-1j; 2-2j 2+3j -1+1j -3] 8 -7 -2 0 [-1 -3+3j -1 1j; -3-3j 2 -1+3j -1+1j; -1 -1-3j -3 -1j; -1j -1-1j 1j -1] 6 -6 -3 0
Douglas Wilhelm Harder
Department of Electrical and Computer Engineering
University of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
Department of Electrical and Computer Engineering
University of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
Website maintained by Douglas Wilhelm Harder