  In the standard geometric approach, the entanglement of a pure state is
$\sin^2\theta$, where $\theta$ is the angle between the entangled state and the
closest separable state of products of normalised qubit states. We consider
here a generalisation of this notion by considering separable states that
consist of products of unnormalised states of different dimension. The distance
between the target entangled state and the closest unnormalised product state
can be interpreted as a measure of the entanglement of the target state. The
components of the closest product state and its norm have an interpretation in
terms of, respectively, the eigenvectors and eigenvalues of the reduced density
matrices arising in the Schmidt decomposition of the state vector. For several
cases where the target state has a large degree of symmetry, we solve the
system of equations analytically, and look specifically at the limit where the
number of qubits is large.
