% create a random tensor system for testing

% tensor dimensions
l=40;
m=10;
n=2;

% elements of the right-hand side
t = trand(l,m,n);
y=rand(m,1);
z=rand(n,1);
z=z/norm(z);

% right-hand side
b = tcontract(t,y,2)*z;

% Householder-rotate the system so that b becomes (b1, 0, ..., 0)'
h = house(b);
t = tlefthouse(h,t,3);	% could also do this along the j dimension
b = lefthouse(h,b);

% reduced homogeneous system
tr = tgetsubtensor(t,2:l,':',':');