Finite-level systems, Hermitian operators, isometries and a novel parametrization of Stiefel and Grassmann manifolds
P. Diţă · Journal of Physics A Mathematical and General · 2005
In this paper, we provide an explicit parametrization of arbitrary n -dimensional Hermitian operators on the Hilbert space , operators that may be considered either as Hamiltonians or density matrices for finite-level quantum systems, the description of which gives a complete solution to the over parametrization problem. It is shown that all the spectral multiplicities are encoded in a flag unitary matrix obtained as an ordered product of special unitary matrices, each one generated by a complex n − k -dimensional unit vector, k = 0, 1, ..., n − 2. As a byproduct, an alternative and simple parametrization of Stiefel and Grassmann manifolds is obtained.