1 function d = Aufgabe2(A, k)
   2 %Aufgabe2 - compute determinant of a matrix by recursion over its minors.
   3 %
   4 %usage
   5 %  d = Aufgabe2(A, k)
   6 %
   7 %input
   8 %  A : (n,n)-matrix.
   9 %  k : Row index in A.
  10 %
  11 %output
  12 %  d : Determinant of A.
  13 %
  14 %description
  15 %  Aufgabe2 computes the determinant of A by summing over the determinants of its
  16 %  minors in row k. The determinants of the minors are computed by recursion where 
  17 %  the trivial case is a (1,1)-matrix.
  18 %
  19 %author
  20 %  buenau@cs.tu-berlin.de
  21 
  22 [n,m] = size(A);
  23 if n ~= m, error('Matrix ist nicht quadratisch'); end
  24 
  25 if n == 1  
  26     % Trivial case.
  27     d = A(1,1);
  28 else
  29     d = 0;
  30     % Sum over minors in row k. 
  31     for j = 1:n
  32       d = d + ((-1).^(k+j) )*A(k,j) * Aufgabe2(A([1:(k-1) (k+1):n], [1:(j-1) (j+1):n]), k-1);
  33     end
  34 end