-This paper proposes a computationally efficient procedure for skew detection and text line position determination in digitized documents, which is based on the cross-correlation between the pixels of vertical lines in a document. The determination of the skew angle in documents is essential in optical character recognition systems. Due to the text skew, each horizontal text line intersects a p...

In this paper, we build the unfolding approach from acyclic sign-skew-symmetric matrices of finite rank to skew-symmetric matrices of infinite rank, which can be regard as an improvement of that in the skew-symmetrizable case. Using this approach, we give a positive answer to the problem by Berenstein, Fomin and Zelevinsky in [6] which asks whether an acyclic signskew-symmetric matrix is always...

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual off-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in th...

An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Severa...

A Coxeter system is called skew-angled if its Coxeter matrix contains no entry equal to 2. In this paper we prove rigidity results for skew-angled Coxeter groups. As a consequence of our results we obtain that skew-angled Coxeter groups are rigid up to diagram twisting.

The contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W . Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W , skew-Ham...

An oriented graph Gσ is a simple undirected graph G with an orientation, which assigns to each edge a direction so that Gσ becomes a directed graph. G is called the underlying graph of Gσ and we denote by S(Gσ) the skew-adjacency matrix of Gσ and its spectrum Sp(Gσ) is called the skew-spectrum of Gσ. In this paper, the coefficients of the characteristic polynomial of the skew-adjacency matrix S...

We present an affirmative answer to Stanley’s zrank problem, namely, the zrank and rank are equal for any skew partition. We show that certain classes of restricted Cauchy matrices are nonsingular and furthermore, the signs depend on the number of zero entries. Similar to notion of the jrank of a skew partition, we give a characterization of the rank in terms of the Giambelli type matrices of t...

We investigate the universality of microscopic eigenvalue correlations for Random Matrix Theories with the global symmetries of the QCD partition function. In this article we analyze the case of real valued chiral Random Matrix Theories (β = 1) by relating the kernel of the correlations functions for β = 1 to the kernel of chiral Random Matrix Theories with complex matrix elements (β = 2), whic...

Computing the exponential of large-scale skew-Hermitian matrices or parts thereof is frequently required in applications. In this work, we consider the task of extracting finite diagonal blocks from a doubly-infinite skew-Hermitian matrix. These matrices usually have unbounded entries which impede the application of many classical techniques from approximation theory. We analyze the decay prope...