  We generalize the concept of the symmetric hyperdeterminants for symmetric
tensors to the E-determinants for general tensors. We show that the
E-determinant inherits many properties of the determinant of a matrix. These
properties include: solvability of polynomial systems, the E-determinat of the
composition of tensors, product formula for the E-determinant of a block
tensor, Hadamard's inequality, Gersgrin's inequality and Minikowski's
inequality. As a simple application, we show that if the leading coefficient
tensor of a polynomial system is a triangular tensor with nonzero diagonal
elements, then the system definitely has a solution. We investigate the
characteristic polynomial of a tensor through the E-determinant. Explicit
formulae for the coefficients of the characteristic polynomial are given when
the dimension is two.
