  A (global) determinantal representation of hypersurface in P^n is a matrix,
whose entries are linear forms in homogeneous coordinates and whose determinant
defines the hypersurface.
  We study the properties of such representations for singular (possibly
reducible or non-reduced) hypersurfaces. In particular, we obtain the
decomposability criteria for determinantal representations of globally
reducible hypersurfaces.
  Further, we classify the determinantal representations in terms of the
corresponding kernel sheaves on $X$. Finally, we extend the results to the case
of symmetric/self-adjoint representations, with implications to hyperbolic
polynomials and generalized Lax conjecture.
