Given an r × r complex matrix T , if T = U |T | is the polar decomposition of T , then, the Aluthge transform is defined by ∆ (T ) = |T |U |T |. Let ∆n(T ) denote the n-times iterated Aluthge transform of T , i.e. ∆0(T ) = T and ∆n(T ) = ∆(∆n−1(T )), n ∈ N. We prove that the sequence {∆n(T )}n∈N converges for every r × r matrix T . This result was conjecturated by Jung, Ko and Pearcy in 2003. W...

Given an r × r complex matrix T , if T = U |T | is the polar decomposition of T , then, the Aluthge transform is defined by ∆ (T ) = |T |U |T |. Let ∆n(T ) denote the n-times iterated Aluthge transform of T , i.e. ∆0(T ) = T and ∆n(T ) = ∆(∆n−1(T )), n ∈ N. We prove that the sequence {∆n(T )}n∈N converges for every r× r diagonalizable matrix T . We show that the limit ∆∞(·) is a map of class C∞...

Given an r × r complex matrix T , if T = U |T | is the polar decomposition of T , then the Aluthge transform is defined by ∆ (T ) = |T |U |T |. Let ∆n(T ) denote the n-times iterated Aluthge transform of T , i.e. ∆0(T ) = T and ∆n(T ) = ∆(∆n−1(T )), n ∈ N. In this paper we make a brief survey on the known properties and applications of the Aluthge trasnsorm, particularly the recent proof of the...

Background: Stabilization of the vital components of neonates before the transform significantly affects their response to treatment. This study aims at evaluating the effects of electronic learning on neonatal stabilization before transform on nurses’ knowledge. Methods: The current quasi-experimental, case-control study of e-learning of neonatal stabilization before the transform was c...

Detecting lines in images using pyramid architecture is the main subject of this paper. The approach is based on the parallel calculation of Hough Transform. A pyramid architecture of size n is a ne-grain architecture with a mesh base of size p n p n processors each holding a single pixel of the image. The pyramid operates in an SIMD mode. Two algorithms for computing the Hough Transform are ex...

The cone beam transform of a tensor field of order m in n >/= 2 dimensions is considered. We prove that the image of a tensor field under this transform is related to a derivative of the n-dimensional Radon transform applied to a projection of the tensor field. Actually the relation we show reduces for m = 0 and n = 3 to the well-known formula of Grangeat. In that sense, the paper contains a ge...

In the last decade a broad literature has arisen studying sparse recovery, the estimation of sparse vectors from low dimensional linear projections. Sparse recovery has a wide variety of applications such as streaming algorithms, image acquisition, and disease testing. A particularly important subclass of sparse recovery is the sparse Fourier transform, which considers the computation of a disc...

Let T be an adjointable operator on a Hilbert $$C^*$$ -module such that has the polar decomposition $$T=U\vert T\vert $$ . For each natural number n, is called $$(n+1)$$ -centered if $$T^k=U^k\vert T^k\vert for $$1\le k\le n+1$$ This paper initiates study of via generalized Aluthge transform and iterative transform. Some new characterizations are provided.

The well-known arbitrary shape detection technology, generalized Hough transform (GHT) has the drawbacks of heavy computations (one-to-many or 1-to-n mapping) and storage requirements (voting space and entry number). Some n-to-1 mapping approaches have been proposed for improving the performance of GHT, such as the FGHT (fast generalized Hough transform), ADPHT (Adaptive dual-point Hough transf...

We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n×n Hermitian matrices as n → ∞. Assuming that the test function of statistics is smooth enough and using the asymptotic formulas by Deift et al for orthogonal polynomials with varying weights, we show first that if the support of the Density of States of ...