The geometric measure of multipartite entanglement and the singular values of a hypermatrix

It is shown that the geometric measure of entanglement of a pure multipartite state satisfies a polynomial equation, generalising the characteristic equation of the matrix of coefficients of a bipartite state. The equation is solved for a class of three-qubit states.Comment: 18 pages. Significant correction made; our results now agree with those of Tamaryan et a