In [11], Köstler and Speicher showed that de Finetti’s theorem on exchangeable sequences has a free analogue if one replaces exchangeability by the stronger condition of invariance of the joint distribution under quantum permutations. In this paper we study sequences of noncommutative random variables whose joint distribution is invariant under quantum orthogonal transformations. We prove a fre...

This work focuses on the correction of both the coecient and the right hand side matrices of the inconsistent matrix equations $AX = B$ and $XC = D$ with orthogonal constraint. By optimal correction approach, a general representation of the orthogonal solution is obtained. This method is tested on two examples to show that the optimal correction is eective and highly accurate.

The Brownian motion of a particle in a harmonic potential, which is simultaneously exposed either to a linear shear flow or to a plane Poiseuille flow is investigated. In the shear plane of both flows the probability distribution of the particle becomes anisotropic and the dynamics is changed in a characteristic manner compared to a trapped particle in a quiescent fluid. The particle distributi...

Based on energy distribution analysis of orthogonal FRIT coefficients, a novel digital image watermark embedding and blind detecting algorithm in ridgelet domain is proposed in this paper. Since the ridgelet transform has directional sensitivity and anisotropy, the image is first partitioned into small pieces and the orthogonal FRIT is applied for each piece to obtain a sparse representation of...

In this paper we consider random block matrices, which generalize the general beta ensembles, which were recently investigated by Dumitriu and Edelmann (2002, 2005). We demonstrate that the eigenvalues of these random matrices can be uniformly approximated by roots of matrix orthogonal polynomials which were investigated independently from the random matrix literature. As a consequence we deriv...