The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of identifying symmetric signings of matrices with natural spectral properties. Our results are twofold: 1. We show NP-completeness for the following three problems: verifying whether a given matrix has a symmetric signing th...

We consider n independent p-dimensional Gaussian vectors with covariance matrix having Toeplitz structure. The aim is two-fold: to test that these have components against a stationary distribution sparse matrix, and also select the support of non-zero entries under alternative hypothesis. Our model assumes values occur in recent past (time-lag less than p/2). build procedures combine sum scan-t...

Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...

We discuss an API that simplifies the specification of a data structure for storing hierarchical matrices (matrices stored recursively by blocks) and the manipulation of such matrices. This work addresses a recent demand for libraries that support such storage of matrices for performance reasons. We believe a move towards such libraries has been slow largely because of the difficulty that has b...

for a symmetric group $g:=sym(n)$ and a conjugacy class $mathcal{x}$ of involutions in $g$, it is known that if the class of involutions does not have a unique fixed point, then - with a few small exceptions - given two elements $a,x in mathcal{x}$, either $angbrac{a,x}$ is isomorphic to the dihedral group $d_{8}$, or there is a further element $y in mathcal{x}$ such that $angbrac{a,y} cong ang...

In this paper we present a corner detection which makes use of eigenvalues of covariance matrices of different support regions over edge points. Edges are first extracted through the use of Canny edge detection, and then determine corners according to eigenvalues product of covariance matrices of the edge at various regions of support. Experimental results show that the proposed method has more...

The computational and/or communication constraints associated with processing large-scale data sets using support vector machines (SVM) in contexts such as distributed networking systems are often prohibitively high, resulting in practitioners of SVM learning algorithms having to apply the algorithm on approximate versions of the kernel matrix induced by a certain degree of data reduction. In t...

Constructive methods for matrices of multihomogeneous (or multigraded) resultants for unmixed systems have been studied by Weyman, Zelevinsky, Sturmfels, Dickenstein and Emiris. We generalize these constructions to mixed systems, whose Newton polytopes are scaled copies of one polytope, thus taking a step towards systems with arbitrary supports. First, we specify matrices whose determinant equa...