I am in need to know the volume of a n-dimensional ellipsoid, but the matrix from which the principal axis are calculated is a singular system. This might sound strange, nevertheless, the explanation in the linked pdf will show you what I am talking about. I guess that the solution is pretty easy for perople with a background from geometry, algebra, or vector-spaces, but I lack of a background in the respective fields of mathematics. Since the question is pretty long I found it more convenient for you to formulate it in a external PDF document. Nevertheless, if forum members wish that I write it in here I will do of course. Any ideas are highly appreciated! Kind Regards, Johannes PS: I asked this question in another forum and offered a dinner to the person who helps me with the solution, but I was almost immediatly thrown out since people found I would ruin the spirit of the forum with that behaviour (so I won't make that same failure here again ;-) ). Thus, just to be clear: the solution to the above problem is the last unsolved part in a larger private reaseach effort in applied statistics. So its not a homework or contract work or anything alike.