Why a n x n vandermonde determinant is'nt equal to 0 for always?

Answer 1

The n x n Vandermonde determinant is the determinant of a n x n Vandermonde matrix. I don't see any reason why it's surprising to have non-zero determinants of these matrices.

Answer 2

Not clear what the VDM determinant is, but some determinants, like strictly positive ones, where all elements x(i,j) > 0 are always positive nonzero. In fact their eigenvalues (lambda > 0) are always positive nonzero. If your VDM has elements x(i,j) > 0, then its determinant will always be positive nonzero.

Zero determinants are special cases for the most part. If two rows/columns are multiples of each other, you'll get the zero value, for example.