Non-Hermitian 4 × 4 invertible matrices
No component greater than 1 in absolute value
[-1+1j -1-1j -1j -1-1j; 1+1j -1-1j -1j -1+1j; -1 -1+1j -1-1j 1 ; -1 1j 1+1j -1j] -2-2j -2+j 1 -j [ -1j 1-1j -1 1+1j; -1+1j -1j 1 1-1j; -1+1j 1+1j -1j -1+1j; -1 1j -1+1j 1+1j] 2-j -1-2j 1+j -1 [ 1+1j -1-1j 1j -1+1j; 1-1j 1-1j -1j 1-1j; 1+1j -1-1j -1-1j 1 ; -1-1j 1-1j -1 1-1j] 1-2j -1-2j 2 2j [-1+1j -1-1j 1-1j -1+1j; -1j 1j 1j 1-1j; -1-1j -1-1j 1-1j -1+1j; 1-1j 1-1j 1j 1j] 1-2j 2j -1+j j [-1-1j 1 1 -1-1j; 1j -1 1 1 ; -1 -1-1j -1-1j -1-1j; -1 -1 1j -1+1j] -2+j -1-2j -1-j j [ 1 1-1j 1+1j 1 ; 1j -1-1j -1j 1 ; -1+1j -1j 1+1j 1+1j; -1j -1+1j -1-1j -1j] -1-2j 2j 1-j 1 [-1-1j -1+1j 1j -1j; 1-1j 1-1j -1 -1-1j; -1 1+1j 1-1j 1j; -1+1j 1-1j -1+1j -1 ] 1-3j -2-j j 1 [-1+1j 1 1 -1+1j; -1-1j 1+1j -1 1-1j; 1 -1 -1j -1j; 1 1+1j 1+1j 1j] 2+j -1+2j -2 1-j [ 1 1+1j 1+1j 1j; 1 1 -1j 1 ; -1+1j -1-1j -1-1j 1-1j; -1-1j 1-1j 1j -1 ] -2-j 2 -j j [ 1-1j -1+1j -1+1j -1+1j; 1-1j 1 1 -1j; -1j -1 -1+1j -1 ; 1j -1 -1-1j 1j] -1-j 1+j j 1 [ 1-1j -1+1j 1-1j -1j; -1j 1 1+1j -1 ; 1+1j -1-1j -1-1j 1-1j; 1 -1j -1j -1 ] 2-j -2-j -1+j 1-j [-1+1j 1+1j 1+1j 1j; 1+1j -1j 1 1 ; -1+1j -1j 1 1j; -1j -1-1j -1j 1j] -1+2j -1-j 1+j 1-j [ 1+1j -1j -1 -1-1j; -1j 1+1j -1 -1-1j; -1+1j 1+1j 1j 1-1j; -1+1j 1-1j -1+1j -1 ] 1+2j -1 j 1 [ -1j 1 1-1j 1j; -1j -1 -1+1j 1 ; 1 -1 1+1j 1j; 1+1j 1 -1+1j 1-1j] -2+j 2-j -2j 1+j [ 1+1j 1+1j -1j -1 ; -1j 1-1j -1+1j -1-1j; -1j -1 -1 1-1j; -1j -1j -1+1j -1j] -1-j 1+j 1 -j [-1-1j 1j 1 -1-1j; 1j 1 -1-1j -1-1j; -1+1j 1 1+1j -1+1j; -1-1j 1j 1 1j] 1+2j -1-2j 1 j [ 1j 1 -1j 1 ; -1 -1+1j -1+1j 1j; -1+1j 1j -1-1j -1j; 1+1j 1-1j 1j 1 ] -2-j 1+j -1+j 1 [ 1 1j 1+1j 1j; -1-1j 1+1j -1 -1-1j; -1+1j 1-1j 1-1j 1-1j; -1+1j 1+1j 1j -1 ] 1-2j -1+j 1+j 1 [ -1j 1+1j -1+1j -1 ; -1 -1j 1j -1-1j; 1+1j -1+1j -1 -1 ; -1+1j -1+1j 1-1j 1-1j] -3j 2-j -1+j -1 [-1-1j 1j 1+1j 1 ; -1j -1 1 -1 ; 1-1j 1+1j -1j 1-1j; -1j 1j -1+1j 1j] -2-j 2 -1+j -1-j [ 1+1j -1j 1+1j -1+1j; -1 1-1j -1j -1 ; -1 1j 1j 1-1j; -1 1-1j -1j -1-1j] 2j -1-j 1-j 1 [ 1+1j 1 -1+1j -1+1j; -1j 1-1j 1 -1+1j; -1-1j -1+1j 1 1+1j; -1-1j 1-1j -1+1j 1-1j] 3 -3j 2+j -1+j [ 1j -1j 1-1j -1j; -1-1j 1+1j 1-1j -1j; -1j 1-1j -1+1j -1 ; -1+1j 1+1j 1-1j 1j] -2+j 1+2j 2j 1-j [ 1-1j -1-1j 1-1j 1j; 1j 1 1+1j -1j; 1j -1+1j -1 1-1j; 1 1+1j 1 1 ] 2-j 2 -1+j -1-j [ -1j 1j -1+1j 1+1j; -1-1j -1j -1-1j 1 ; -1j 1-1j -1 1 ; 1-1j -1 1-1j -1j] 2-j -2-j -2j -1+j [ 1+1j -1 1+1j -1j; 1-1j 1-1j 1-1j 1+1j; -1j 1 -1j 1 ; -1+1j 1j 1+1j 1 ] 2+j 2 -2j -1 [ 1 1 -1+1j 1-1j; -1-1j -1+1j 1 1+1j; 1 -1-1j -1-1j -1j; 1j 1 -1j 1-1j] -2j 1 j -1 [ 1+1j -1+1j 1 -1j; -1+1j -1-1j -1j -1 ; 1j 1+1j -1+1j 1 ; 1+1j 1 -1 -1+1j] -2+2j 1+j -j -1 [ 1+1j -1+1j 1j -1-1j; -1 1-1j 1+1j -1+1j; 1-1j 1-1j 1j 1+1j; 1j 1+1j -1 -1-1j] -2+j 2 -2j 1+j [-1-1j 1j 1 -1j; 1 -1+1j 1-1j 1 ; -1-1j -1j -1-1j 1j; 1j -1 -1-1j 1+1j] -1+j -1-j -j j [-1+1j -1 -1 -1+1j; -1+1j -1-1j -1 1+1j; -1-1j 1 -1 1j; -1+1j -1j -1-1j -1+1j] -2+j -2+j 1-j -1 [-1-1j 1 -1-1j -1 ; -1 1 -1 1 ; 1+1j -1j 1 1 ; 1 -1j 1 -1j] 1-j -1-j 1-j j [ -1j -1 -1-1j -1j; -1 -1+1j 1j 1 ; -1j -1-1j 1j 1-1j; -1-1j -1 1j -1+1j] -1+2j -1-j 1+j -1 [ -1j 1 -1-1j -1j; 1j -1j -1j -1j; -1j -1 -1j 1 ; 1j 1-1j -1j -1-1j] -1-2j -2j -1 1 [-1-1j -1-1j 1j -1 ; -1+1j -1+1j 1+1j -1 ; 1-1j -1-1j -1j 1-1j; -1+1j 1+1j -1+1j -1j] -2 1-j -j -1 [-1-1j -1j -1 1+1j; 1j 1j 1+1j -1+1j; -1j 1-1j -1j 1-1j; -1 -1 -1 -1 ] -2-j -1+j -j 1 [ 1 -1j -1-1j -1j; 1j 1+1j -1j 1j; 1 1-1j 1j -1 ; 1j -1 -1+1j 1 ] 2-j 2j 2 -1+j [ 1j 1-1j -1-1j -1+1j; -1 -1 1-1j -1-1j; -1+1j 1+1j 1+1j -1j; 1j -1+1j -1j -1+1j] 2+j -2+j j -1 [ 1+1j 1-1j -1-1j 1 ; -1j -1 1j 1-1j; -1+1j -1+1j 1-1j 1-1j; -1+1j -1-1j 1 -1 ] -1+2j 1-j -1-j 1 [ 1+1j -1 -1-1j -1-1j; 1 -1+1j 1-1j 1-1j; 1-1j -1+1j -1j -1+1j; 1j -1j 1j 1-1j] 1-2j 2j j -j [-1+1j 1+1j -1-1j -1+1j; -1 1 -1j 1j; 1+1j -1+1j 1+1j 1-1j; -1j -1-1j -1j 1+1j] -2+2j 2+j 1-j 1+j [-1-1j 1 1j -1+1j; 1+1j -1 -1+1j -1-1j; 1+1j 1+1j 1j -1-1j; -1+1j -1+1j 1+1j -1-1j] -2-j 1-2j -2 2j [ 1j 1-1j 1-1j -1-1j; -1+1j 1j 1+1j 1j; -1-1j 1-1j -1j -1j; -1j 1 1 1-1j] 1+2j -2j -1 1 [ 1 1+1j 1+1j -1+1j; 1-1j 1 -1-1j -1+1j; -1j -1j -1-1j -1j; 1j -1 1j -1-1j] 2-j -2-j -1 1 [ 1j 1 1 1-1j; 1+1j 1 -1+1j 1+1j; -1+1j -1-1j 1 -1-1j; -1+1j -1+1j -1-1j -1 ] 2+j -2-j 1+2j -j [ -1j 1 -1+1j 1j; 1j -1 1 1+1j; -1-1j -1 -1+1j 1j; 1 -1j -1j -1-1j] -2 -1-j -1 1 [ -1j 1-1j -1j -1j; 1-1j -1j 1 -1+1j; -1 -1 -1-1j 1 ; 1-1j 1-1j 1+1j -1j] -1-2j -2j 1 -1 [ 1-1j 1 1j 1j; 1 1-1j 1 1j; -1j 1j 1+1j -1j; -1 1 -1+1j 1-1j] 2-j 2+j 1-j -1-j [ 1-1j -1j -1 -1 ; -1-1j 1 1+1j -1+1j; 1-1j -1+1j -1 -1-1j; -1 1j -1 1+1j] 1+2j 1 -j -j
No component greater than 2 in absolute value
[-2 -1+2j 1-2j -2 ; -1 -2-2j 1j 1-1j; -1-1j -1-1j 2+2j 2+1j; 1-2j 1-2j 1+2j -2 ] 2+3j -3-2j -2+j -1-2j [ 1-2j -1j -2+1j -1+1j; -1 -1j -1 2 ; -1-1j -1+1j 1j 1j; 2-2j -2-2j 2-2j -1+2j] 1+2j -2+j -2j 1-j [-2-1j 2j -1 1-1j; 1+2j 2j -1-1j -2+1j; -2+1j 1 -2 1j; -2-2j -1+1j -2-1j 2+1j] -2+2j -1-2j 1+j j [ 2j -2j -2+1j 1+2j; 1-1j 1+1j 1j 1-1j; 1+1j 1-1j 1+1j 1-2j; 1j -1 1 2+1j] 1+3j 3j 2 1-j [ 1j -1 1-2j 2-1j; 1-2j 1j -1-2j 1-2j; -1j -1+1j -1-1j -1j; 1-1j 2 1+1j -1+1j] -2+2j -2+j 2 -j [ 1-1j 2+1j 1-2j -1-1j; 1-2j -2 1+1j -1j; 1+1j 1+2j 2 2-1j; -2+1j -1 -1+2j 1j] 4+j -3 -1-j 1 [ 1-1j 2+2j -1+2j 1+1j; 2-2j 1-1j 1-1j -1 ; -1+1j -1 1-2j 1j; -2+1j -2+2j -1 1j] 3-2j 1-2j -2+j 1
No component greater than 3 in absolute value
[-3 1+1j 1 3+1j; 2-2j 1-1j 1 1+2j; -1-3j -3j 2-2j 3-2j; 2+2j 3j 1+2j -2+0j] 4-j -4-j -2-2j j
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