  The study of multipartite entanglement is not only interesting but also
important due to its wide application in quantum information processing.
However, the complicated structure of the Hilbert space for many parties makes
multipartite entanglement extremely complicated. It is then worth studying the
structure of the Hilbert space itself. In this work, we provide a way to study
the structure of SLOCC-equivalence and to determine the number free parameters
for SLOCC-equivalent classes. Additionally, two different entanglement
witnesses are introduced. The method matches well the existing results, and can
make predictions for more-qubit systems.
