Funes el memorioso

% positive part
>> P=[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1;
1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0; 
1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1; 
1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1; 
1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1; 
1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0; 
1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0; 
1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0; 
1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1; 
1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0; 
1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1]; 

% negative part
>> N = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0;
0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1;
0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0;
0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0;
0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0;
0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1;
0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1;
0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1;
0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0;
0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1;
0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0];

% zero matrix
>> Z = zeros(size(N)(1));

% an signed adjacency matrix of a complete bipartite graph
>> H = [Z, P-N; P'-N', Z];

% eigenvalues of a signed adjacency matrix
>> eig(H)
ans =

  -3.4641
  -3.4641
  -3.4641
  -3.4641
  -3.4641
  -3.4641
  -3.4641
  -3.4641
  -3.4641
  -3.4641
  -3.4641
  -3.4641
   3.4641
   3.4641
   3.4641
   3.4641
   3.4641
   3.4641
   3.4641
   3.4641
   3.4641
   3.4641
   3.4641
   3.4641

% check that it's a sqrt(12)
>> 3.4641^2
ans =  12.000

% the leading principal sub-matrix of size 12
>> A12 = eig(H(1:12, 1:12)), size(A12)
A12 =

   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0

ans =

   12    1

% the leading principal sub-matrix of size 13
>> A13 = eig(H(1:13, 1:13)), size(A13)
A13 =

  -3.46410
   0.00000
   0.00000
   0.00000
   0.00000
   0.00000
   0.00000
   0.00000
   0.00000
   0.00000
   0.00000
   0.00000
   3.46410

ans =

   13    1

% the leading principal sub-matrix of size 14
>> A14 = eig(H(1:14, 1:14)), size(A14)
A14 =

  -3.4641e+00
  -3.4641e+00
  -2.2869e-16
  -5.1835e-17
  -3.1072e-32
  -9.8437e-33
  -9.1270e-34
  -1.6678e-48
   6.7204e-34
   2.6380e-33
   5.5511e-17
   1.0011e-16
   3.4641e+00
   3.4641e+00

ans =

   14    1

% the leading principal sub-matrix of size 15
>> A15 = eig(H(1:15, 1:15)), size(A15)
A15 =

  -3.4641e+00
  -3.4641e+00
  -3.4641e+00
  -1.2569e-16
  -5.2487e-17
  -2.7846e-17
   8.3967e-19
   2.9178e-17
   1.3011e-16
   2.6577e-16
   6.1994e-16
   7.9764e-16
   3.4641e+00
   3.4641e+00
   3.4641e+00

ans =

   15    1

% the leading principal sub-matrix of size 16
>> A16 = eig(H(1:16, 1:16)), size(A16)
A16 =

  -3.4641e+00
  -3.4641e+00
  -3.4641e+00
  -3.4641e+00
  -4.8088e-16
  -3.2142e-16
  -1.4036e-16
   1.4234e-17
   1.1284e-16
   2.6229e-16
   4.1426e-16
   4.6066e-16
   3.4641e+00
   3.4641e+00
   3.4641e+00
   3.4641e+00

ans =

   16    1