Skip to the content of the web site.

Hermitian 3 × 3 singular matrices

No component greater than 1 in absolute value

 [-1  -1       -1j; -1     -1    -1j;    1j     1j  -1] -3 0 0
 [ 1     1j  -1   ;   -1j   1     1j; -1       -1j   1]  3 0 0
 [ 1     1j    -1j;   -1j   1  -1   ;    1j  -1      1]  3 0 0
 [-1  -1       -1j; -1     -1    -1j;    1j     1j  -1] -3 0 0
 [ 1    -1j   1   ;    1j   1     1j;  1       -1j   1]  3 0 0
 [-1   1       -1j;  1     -1     1j;    1j    -1j  -1] -3 0 0
 [-1  -1        1j; -1     -1     1j;   -1j    -1j  -1] -3 0 0
 [ 1  -1       -1j; -1      1     1j;    1j    -1j   1]  3 0 0
 [ 1   1+1j   1-1j;  1-1j  -1     1j;  1+1j    -1j  -1] -3 2 0
 [-1   1      1+1j;  1     -1  -1-1j;  1-1j  -1+1j   1] -3 2 0
 [-1  -1-1j     1j; -1+1j   1   1+1j;   -1j   1-1j  -1] -3 2 0
 [ 1   1+1j     1j;  1-1j  -1   1+1j;   -1j   1-1j   1]  3 -2 0
 [-1  -1+1j   1-1j; -1-1j   1  -1   ;  1+1j  -1      1]  3 -2 0
 [ 1   1+1j   1   ;  1-1j  -1   1-1j;  1      1+1j   1]  3 -2 0
 [-1  -1+1j   1+1j; -1-1j   1    -1j;  1-1j     1j   1]  3 -2 0
 [-1  -1+1j   1+1j; -1-1j   1    -1j;  1-1j     1j   1]  3 -2 0
 [ 1   1-1j   1+1j;  1+1j  -1    -1j;  1-1j     1j  -1] -3 2 0
 [ 1   1-1j  -1+1j;  1+1j  -1   1   ; -1-1j   1     -1] -3 2 0
 [ 1   1-1j  -1   ;  1+1j  -1  -1-1j; -1     -1+1j   1]  3 -2 0
 [ 1  -1-1j   1   ; -1+1j  -1  -1+1j;  1     -1-1j   1]  3 -2 0
 [ 1   1+1j     1j;  1-1j  -1   1+1j;   -1j   1-1j   1]  3 -2 0
 [ 1     1j   1-1j;   -1j   1  -1-1j;  1+1j  -1+1j  -1]  3 -2 0
 [ 1   1+1j   1+1j;  1-1j  -1  -1   ;  1-1j  -1     -1] -3 2 0
 [ 1   1     -1+1j;  1      1  -1+1j; -1-1j  -1-1j  -1]  3 -2 0
 [ 1    -1j   1+1j;    1j   1  -1+1j;  1-1j  -1-1j  -1]  3 -2 0
 [-1  -1     -1+1j; -1     -1  -1+1j; -1-1j  -1-1j   1] -3 2 0
 [ 1   1-1j  -1-1j;  1+1j  -1     1j; -1+1j    -1j  -1] -3 2 0
 [ 1   1+1j   1-1j;  1-1j  -1     1j;  1+1j    -1j  -1] -3 2 0
 [ 1   1-1j    -1j;  1+1j  -1   1-1j;    1j   1+1j   1]  3 -2 0
 [-1  -1+1j  -1   ; -1-1j   1  -1-1j; -1     -1+1j  -1] -3 2 0
 [ 1   1-1j  -1-1j;  1+1j  -1     1j; -1+1j    -1j  -1] -3 2 0
 [-1     1j  -1-1j;   -1j  -1   1-1j; -1+1j   1+1j   1] -3 2 0
 [-1  -1     -1-1j; -1     -1  -1-1j; -1+1j  -1+1j   1] -3 2 0
 [-1   1-1j    -1j;  1+1j   1  -1+1j;    1j  -1-1j  -1] -3 2 0
 [-1  -1     -1-1j; -1     -1  -1-1j; -1+1j  -1+1j   1] -3 2 0
 [-1   1-1j     1j;  1+1j   1   1-1j;   -1j   1+1j  -1] -3 2 0
 [-1     1j   1-1j;   -1j  -1   1+1j;  1+1j   1-1j   1] -3 2 0
 [-1  -1-1j   1+1j; -1+1j   1  -1   ;  1-1j  -1      1]  3 -2 0
 [ 1  -1+1j  -1+1j; -1-1j  -1  -1   ; -1-1j  -1     -1] -3 2 0
 [-1   1+1j   1+1j;  1-1j   1   1   ;  1-1j   1      1]  3 -2 0
 [-1  -1-1j   1-1j; -1+1j   1     1j;  1+1j    -1j   1]  3 -2 0
 [-1    -1j  -1+1j;    1j  -1   1+1j; -1-1j   1-1j   1] -3 2 0
 [-1   1      1-1j;  1     -1  -1+1j;  1+1j  -1-1j   1] -3 2 0
 [-1  -1+1j  -1   ; -1-1j   1  -1-1j; -1     -1+1j  -1] -3 2 0
 [ 1   1      1-1j;  1      1   1-1j;  1+1j   1+1j  -1]  3 -2 0

No component greater than 2 in absolute value

 [ 2  -1+1j   2   ; -1-1j   1  -1-1j;  2     -1+1j   2]  5 0 0
 [ 2   1+1j   2   ;  1-1j   1   1-1j;  2      1+1j   2]  5 0 0
 [ 2   1      1+1j;  1     -1  -1+2j;  1-1j  -1-2j  -2] -4 3 0
 [ 1  -2+2j   2   ; -2-2j  -2    -2j;  2        2j   2]  5 -4 0
 [-1   1      1   ;  1     -2  -1-1j;  1     -1+1j  -2] -4 -1 0
 [ 2   2     -2+2j;  2     -2   2   ; -2-2j   2     -1] -5 4 0
 [ 2   1-2j    -1j;  1+2j  -2  -2+1j;    1j  -2-1j  -2] -5 3 0
 [ 1   1+1j  -1-2j;  1-1j  -1     2j; -1+2j    -2j  -1] -4 3 0
 [-2   1+1j   2+2j;  1-1j  -1  -2   ;  2-2j  -2      1] -5 3 0
 [ 1   2-1j  -1-2j;  2+1j   2    -2j; -1+2j     2j   2]  6 -1 0
 [-1    -1j  -2-2j;    1j  -1  -2+2j; -2+2j  -2-2j  -2] -6 2 0
 [-2   1+2j   1+2j;  1-2j  -2  -1   ;  1-2j  -1      2] -5 3 0
 [-2    -1j   2-1j;    1j   2  -1-2j;  2+1j  -1+2j  -2] -5 3 0
 [-1  -1+1j    -2j; -1-1j   1   2+1j;    2j   2-1j  -1] -4 3 0
 [ 2    -1j     1j;    1j  -1  -2   ;   -1j  -2     -1] -3 3 0
 [ 2  -1-2j   1   ; -1+2j  -2   1-2j;  1      1+2j  -2] -5 3 0
 [ 2  -2     -2-2j; -2     -2    -2j; -2+2j     2j  -1] -5 4 0
 [-2   2+2j   1+1j;  2-2j  -2  -2   ;  1-1j  -2     -1] -6 1 0
 [ 1   1-1j   2+2j;  1+1j  -2   2-2j;  2-2j   2+2j  -2] -6 3 0
 [-2  -2-1j   1+1j; -2+1j  -1    -1j;  1-1j     1j   2] -4 3 0
 [-2   2-2j  -2+2j;  2+2j  -2   1-1j; -2-2j   1+1j   1] -6 3 0
 [-2   1+2j   1   ;  1-2j  -2  -1+2j;  1     -1-2j   2] -5 3 0
 [ 2   2+2j  -2+2j;  2-2j  -1   1+1j; -2-2j   1-1j   2]  6 -3 0
 [ 1    -2j  -2-2j;    2j  -1  -1+1j; -2+2j  -1-1j  -2] -5 3 0
 [ 1    -2j   1+1j;    2j   1   1+2j;  1-1j   1-2j  -1]  4 -3 0
 [ 2  -2+1j   1+1j; -2-1j   1   1   ;  1-1j   1     -2]  4 -3 0
 [ 1   1-1j   1-1j;  1+1j  -2   2   ;  1+1j   2      2]  4 -3 0

No component greater than 3 in absolute value

 [ 2   2      1+3j;  2      2   1+3j;  1-3j   1-3j   3]  8 -1 0
 [-1     3j   3+2j;   -3j  -3     3j;  3-2j    -3j  -1] -8 3 0
 [ 1   3+1j    -2j;  3-1j   2  -2-2j;    2j  -2+2j   2]  7 -2 0
 [-2  -1       -1j; -1     -2     1j;    1j    -1j  -2] -3 -3 0
 [ 1   1-1j   1+2j;  1+1j  -1   2   ;  1-2j   2     -1] -4 3 0
 [-1   2+2j   1+2j;  2-2j  -3  -3-1j;  1-2j  -3+1j  -3] -8 1 0
 [-2  -1-1j   1+1j; -1+1j   1   3   ;  1-1j   3      1] -4 4 0
 [ 1   1+2j    -1j;  1-2j   2   1-1j;    1j   1+1j  -2]  4 -3 0
 [-3  -1+1j  -2+1j; -1-1j  -1  -1-1j; -2-1j  -1+1j  -3] -6 -1 0
 [ 1   1+1j   2-1j;  1-1j  -1  -2   ;  2+1j  -2     -1] -4 3 0
 [-3  -1-1j  -1-2j; -1+1j  -2  -1+1j; -1+2j  -1-1j  -3] -6 -2 0
 [ 2   1-3j   3+3j;  1+3j   3  -1+2j;  3-3j  -1-2j  -1]  8 -4 0
 [-2  -1+1j    -2j; -1-1j  -1   1-1j;    2j   1+1j   2] -4 3 0
 [-1     2j    -2j;   -2j  -3   3+1j;    2j   3-1j  -2] -7 1 0
 [ 1   3+2j   2+1j;  3-2j  -2   2+2j;  2-1j   2-2j   2]  6 -5 0
 [ 2   3-1j   1-1j;  3+1j   2   2+2j;  1+1j   2-2j  -2]  6 -4 0
 [ 2   1+3j    -1j;  1-3j  -2   2+3j;    1j   2-3j  -3] -7 4 0
 [ 2   2      1+1j;  2      3   2+2j;  1-1j   2-2j   3]  7 1 0
 [ 2  -3      1   ; -3     -3    -3j;  1        3j  -1] -6 4 0
 [-2   1+3j  -1+1j;  1-3j  -1  -1-2j; -1-1j  -1+2j  -1] -6 2 0
 [ 1   1-1j   2+2j;  1+1j  -3    -1j;  2-2j     1j   3]  5 -4 0
 [-2  -2        2j; -2     -1   2+2j;   -2j   2-2j   2] -5 4 0
 [ 1  -1+2j   2-3j; -1-2j  -1   1+2j;  2+3j   1-2j  -2] -6 4 0
 [ 3  -1+1j  -1+3j; -1-1j  -1   2-1j; -1-3j   2+1j   3]  7 -2 0

No component greater than 4 in absolute value

 [-2  -2+3j   3-3j; -2-3j  -2   3   ;  3+3j   3     -4] -10 2 0
 [-3   3+1j  -2+3j;  3-1j   1    -3j; -2-3j     3j  -4] -9 3 0
 [ 1  -1-4j    -2j; -1+4j   2   2-1j;    2j   2+1j   1]  7 -3 0
 [ 1   4-3j    -3j;  4+3j  -2    -3j;    3j     3j   3]  8 -6 0
 [-4     3j   3-3j;   -3j   1  -3+2j;  3+3j  -3-2j   4]  8 -7 0
 [-3  -3-2j   3+2j; -3+2j   4  -4   ;  3-2j  -4      4]  10 -5 0
 [-3  -1-1j   1+1j; -1+1j  -4    -2j;  1-1j     2j  -2] -6 -3 0
 [ 2   1-3j   1+2j;  1+3j   4  -2   ;  1-2j  -2     -4]  7 -5 0
 [ 1  -1+2j  -1+2j; -1-2j   3   2-3j; -1-2j   2+3j  -4] -6 6 0
 [ 2  -2-2j   2+2j; -2+2j  -1  -1+4j;  2-2j  -1-4j  -1] -6 6 0
 [-3  -4-3j  -1-1j; -4+3j   3  -2+4j; -1+1j  -2-4j   1]  8 -7 0
 [-1    -3j   1-1j;    3j  -4  -3+2j;  1+1j  -3-2j   3] -7 5 0
 [-3   4+2j   3+4j;  4-2j  -1   1-1j;  3-4j   1+1j   3] -8 7 0
 [ 2  -4      1-1j; -4      1  -2+2j;  1+1j  -2-2j   1]  7 -3 0
 [ 4   4-4j   4+4j;  4+4j  -4    -4j;  4-4j     4j  -4] -12 8 0
 [ 3  -1+1j   4+4j; -1-1j  -2   4   ;  4-4j   4      2]  9 -6 0

No component greater than 5 in absolute value

 [ 3  -3+1j  -3-2j; -3-1j  -2   5+3j; -3+2j   5-3j   3]  10 -6 0
 [-5  -1+5j  -1   ; -1-5j   5  -2-4j; -1     -2+4j   1]  9 -8 0
 [ 5     4j  -2   ;   -4j  -2   3-3j; -2      3+3j  -5] -9 7 0
 [ 4   1+1j   3+1j;  1-1j  -1   4+1j;  3-1j   4-1j  -5] -8 6 0
 [-1  -2+3j  -3-5j; -2-3j   1   2+2j; -3+5j   2-2j   1]  8 -7 0
 [-3  -3+1j     1j; -3-1j  -5  -1+3j;   -1j  -1-3j  -3] -9 -2 0
 [-3   2-5j   1-1j;  2+5j  -3  -1-5j;  1+1j  -1+5j   2] -10 6 0
 [-1  -1+1j  -3-4j; -1-1j   1  -2+2j; -3+4j  -2-2j   5]  9 -4 0
 [ 3   2-3j  -1-2j;  2+3j   3   4-1j; -1+2j   4+1j  -5]  8 -7 0
 [-5  -1+5j  -2-3j; -1-5j   2   5-5j; -2+3j   5+5j  -1] -12 8 0
 [-5   4+1j  -5+2j;  4-1j  -1     1j; -5-2j    -1j   5] -9 8 0