Numerical sparse basis for base bla bla bla

gistfile1.txt

Z_B_2 = [0,0,1,0;0,0,0,1];
X_B_2 = Z_B_2';
P_B_2 = X_B_2*Z_B_2;

Z_B_1 = [1,0,0,0;0,1,0,0];
X_B_1 = Z_B_1';
P_B_1 = X_B_1*Z_B_1;

Z_I = [1,0,0,0;0,0,1,0;0,sqrt(2)/2,0,sqrt(2)/2];
X_I = Z_I';
P_I = X_I*Z_I;

[U,S,V] = svd((P_I*X_B_2)')

#some of them
Z_A = [0,0,1,0;0,0,0,1];
X_A = Z_A';
P_A = X_A*Z_A;

Z_B = [1,0,0,0;0,0,1,0;0,sqrt(2)/2,0,sqrt(2)/2];
X_B = Z_B';
P_B = X_B*Z_B;

[U,S,V] = svd(Z_A*P_B)


#all of them
Z_B = [0,0,1,0;0,0,0,1];
X_B = Z_B';
P_B = X_B*Z_B;

Z_A = [1,0,0,0;0,1,0,0;0,0,1,0;];
X_A = Z_A';
P_A = X_A*Z_A;

[U,S,V] = svd(Z_A*P_B)

Serious stuff now
tol = 1e-7;
n = 10;
n_A = unidrnd(n-1);
n_B = unidrnd(n-1);
n_C = unidrnd(n-1);
X_B = orth(rand(n,n))(:,1:n_B);
X_A = orth(rand(n,n))(:,1:n_A);
X_C = orth(rand(n,n))(:,1:n_C);
Z_C = X_C';
Z_B = X_B';
Z_A = X_A';
P_A = X_A*Z_A;
P_B = X_B*Z_B;
[U,S,V] = svd((Z_A*P_B));

I = eye(n,n);

X_B_intersect_C = null([I-X_B*Z_B;I-X_C*Z_C]);
X_A_plus_B_intersect_C = orth([X_A,X_B_intersect_C])

X_A_plus_B = orth([X_A,X_B]);
X_A_plus_C = orth([X_A,X_C]);
X_A_plus_B_intersect_A_plus_C = null([I-X_A_plus_B*X_A_plus_B';I-X_A_plus_C*X_A_plus_C'])