> restart;
> with(LinearAlgebra): printlevel:=0;
> qr_zerlegung:=proc(A)
> local n,j,nor,k,i,summe;
global v,c;
> # option trace;
n:=RowDimension(A);
v:=Vector(n); c:=Vector(n);
for j from 1 to n-1 do
   nor:=0;
   for k from j to n do nor := nor + A[k,j]*A[k,j]; end do;
   nor:=sqrt(nor);
   if nor=0 then v[j]:=0;
   else
      c[j]:=1.0/(nor*nor + nor*abs(A[j,j]));
      if A[j,j] <0 then nor:=-nor end if;
      v[j]:=A[j,j]+nor;
      A[j,j]:=-nor;
      for k from j+1 to n do
          summe:=v[j]*A[j,k];
          for i from j+1 to n do summe:=summe + A[i,j]*A[i,k]; end do;
          summe:= summe*c[j];
          A[j,k]:=A[j,k]-v[j]*summe;
          for i from j+1 to n do A[i,k]:= A[i,k]-A[i,j]*summe; end do;
      end do;
   end if;
end do;
print(A,v,c);
end proc:
> 
> 
> 
A:=Matrix([[3.,-9.,7.], [-4.,-13.,-1.],[0.,-20.,-35.]]);
> qr_zerlegung(A);
>