An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U ( N ) (or O ( N )). An ensemble of symmetric unistochastic matrices is obtained with use of unitary symmetric matrices pertaining to the circular orthogonal ensemble. We study the distribution of complex eigenvalues of bistochastic, unistochastic and orthostochastic matrices in the complex plane. We compute averages (entropy, traces) over the ensembles of unistochastic matrices and present inequalities concerning the entropies of products of bistochastic matrices.An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U ( N ) (or O ( N )). An ensemble of symmetric unistochastic matrices is obtained with use of unitary symmetric matrices pertaining to the circular orthogonal ensemble. We study the distribution of complex eigenvalues of bistochastic, unistochastic and orthostochastic matrices in the complex plane. We compute averages (entropy, traces) over the ensembles of unistochastic matrices and present inequalities concerning the entropies of products of bistochastic matrices.

arXiv:nlin/0112036Journal of Physics A Mathematical and GeneralMar 13, 200368 citations

Conditional probabilities on orthomodular lattices

Gianni Cassinelli, Piero Truini

Reports on Mathematical PhysicsAug 1, 19849 citations

Products of Random Matrices

A. Crisanti, Giovanni Paladin, Angelo Vulpiani

Springer series in solid-state sciencesJan 1, 1993302 citations

Geometry of density matrices. I. Definitions, N matrices and 1 matrices

John E. Harriman

Density matrices defined with respect to a finite basis set are considered as elements in a vector space. A basis set is introduced in the space whose elements are Hermitian matrices. By a suitable transformation of the basis, one component only will contribute to the trace, so the space of unit trace matrices is a translated linear subspace. The positivity constraint is then examined in terms of distance from a multiple of the unit matrix, which is in the interior of the set of density matrices. The boundary of this set is shown to lie between two concentric hyperspheres. The set whose elements are $N$ -representable 1 matrices has similar properties.Density matrices defined with respect to a finite basis set are considered as elements in a vector space. A basis set is introduced in the space whose elements are Hermitian matrices. By a suitable transformation of the basis, one component only will contribute to the trace, so the space of unit trace matrices is a translated linear subspace. The positivity constraint is then examined in terms of distance from a multiple of the unit matrix, which is in the interior of the set of density matrices. The boundary of this set is shown to lie between two concentric hyperspheres. The set whose elements are $N$-representable 1 matrices has similar properties.

Physical Review AApr 1, 1978105 citations

Set Of

3\times 3

Orthostochastic Matrices

N

-representable 1 matrices has similar properties.