%========Gram-Schmidt Process==============================================
function e=gramsmt
k=input('Define the number of vectors to be normalized\n\n');
s=input('Define the dimensions of vectors to be normalized\n\n');
v=zeros(s,k);
for j=1:k
    for i=1:s
        str=sprintf('Give the #%d coordinate of the #%d vector\n',i,j);
        disp(str);
        v(i,j)=input(' ');
    end
end
%===Every column of matrix V forms a vector Vj=============================
u=zeros(s,k);
e=zeros(s,k);
u(:,1)=v(:,1);
e(:,1)=u(:,1)./(norm(u(:,1),2));
for i=2:k
    sum=zeros(s,1);
    for j=1:i-1
        sum=sum+proj(u(:,j),v(:,i));
    end
    u(:,i)=v(:,i)-sum;
    e(:,i)=u(:,i)./(norm(u(:,i),2));
end
%==========================================================================