… In this section we shall derive a polynomial expression in the coefficients of a multipartite
pure state, the roots of which include the geometric measure of entanglement of the state.
This is directly analogous to the characteristic polynomial of a square matrix, which can be
used to determine the Schmidt coefficients of an ordinary bipartite vector. … Theorem 3.2
establishes the existence of a polynomial equation satisfied by the singular values of a
hypermatrix, but does not give a fully explicit description of this equation. We will now show …