   function [y] = hoApp(V,bet,x) 
%% function [y] = hoApp(V,bet,x) 
%% applies householder transform to 
%% a vector x
[m,n] = size(V);
y = x(:);
v = zeros(m,1);
for k=1:n 
   v(k) = 1;
   v(k+1:m) = V(k+1:m,k) ;
   t  = bet(k) * v(k:m)'*y(k:m);
   y(k:m) = y(k:m) - t*v(k:m); 
end
