Reading about matrices and determinants I am wondering about the following concept:
How valid is to compare the determinants of matrices with different dimensions? e.g. compare a determinant $D1$ derived from a $N\times N$ matrix with the determinant $D2$ derived from a $M\times M$ matrix.
I've read that the determinant represents the volume of the $N-$dimensional object that is defined by the elements of the matrix.
If this is correct then comparing volumes of different "objects" doesn't sound as incorrect. But having in mind that these "objects" came from two different spaces (a $N-$dimensional and a $M-$dimensional) how valid is that?