We provide an elementary proof for a theorem due to Petz and Réffy which states that for a random n × n unitary matrix with distribution given by the Haar measure on the unitary group U(n), the upper left (or any other) k × k submatrix converges in distribution, after multiplying by a normalization factor √ n and as n → ∞, to a matrix of independent complex Gaussian random variables with mean 0...

Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices An and Bn rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix Un (i.e. An + U∗ nBnUn) is studied in the limit of large matrix order n. Convergence in probability to a limiting nonrandom measure is established. A functional equation for the St...

Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...

tion 14 will generally contain more internal vertices than the AND of those same functions with product terms. Therefore, we computed the probability values of the fundamental equivalence relations for the ISCAS benchmark circuits c432 and c880 for outputs 421gat and 878gat respectively. Tables 4 and 5 contain the results of these computations. The algorithm used to compute the probabilities is...

In this paper, a new face recognition system based on Wavelet transform (HWT) and Principal Component Analysis (PCA) is presented. The image face is preprocessed and detected. The Haar wavelet is used to form the coefficient matrix for the detected face. The image feature vector is obtained by computing PCA for the coefficient matrix of DWT. A comparison between the proposed recognition system ...

Results from the theory of the generalized hypergeometric functions of matrix argument, and the related zonal polynomials, are used to develop a new approach to study the asymptotic distributions of linear functions of uniformly distributed random matrices from the classical compact matrix groups. In particular, we provide a new approach for proving the following result of D’Aristotile, Diaconi...

In this paper we present the first practical method for importance sampling functions represented as spherical harmonics (SH). Given a spherical probability density function (PDF) represented as a vector of SH coefficients, our method warps an input point set to match the target PDF using hierarchical sample warping. Our approach is efficient and produces high quality sample distributions. As a...