Related papers: Note on regions containing eigenvalues of a matrix
We consider the problem of recovering a unitary eigendecomposition of a complex unitary matrix from that of its embedded real-valued formulation. Such formulations arise naturally in scientific computing workflows that employ…
We consider real non-symmetric matrices and their factorisation as a product of real symmetric matrices. The number of complex eigenvalues of the original matrix reveals restrictions on such factorisations as we shall prove.
We propose a method for obtaining rigorous and accurate upper and lower bounds on the eigenvalues of ordinary and partial differential operators in bounded regions of Euclidean space. It uses a boundary condition homotopy method starting…
A novel local depth definition, $\beta$-integrated local depth ($\beta$-ILD), is proposed as a generalization of the local depth introduced by Paindaveine and Van Bever \cite{paindaveine2013depth}, designed to quantify the local centrality…
In this paper, the exact distribution of the largest eigenvalue of a singular random matrix for multivariate analysis of variance (MANOVA) is discussed. The key to developing the distribution theory of eigenvalues of a singular random…
Divergences are fundamental to the information criteria that underpin most signal processing algorithms. The alpha-beta family of divergences, designed for non-negative data, offers a versatile framework that parameterizes and continuously…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
In this paper, we introduce a particular class of matrices. We study the concept of a matrix to be \emph{balanced}. We study some properties of this concept in the context of matrix operations. We examine the behaviour of various matrix…
It has been recently shown that a large class of balanced graph cuts allows for an exact relaxation into a nonlinear eigenproblem. We review briefly some of these results and propose a family of algorithms to compute nonlinear eigenvectors…
In this text, we consider an N by N random matrix X such that all but o(N) rows of X have W non identically zero entries, the other rows having lass than $W$ entries (such as, for example, standard or cyclic band matrices). We always…
This is a brief survey of classical and recent results about the typical behavior of eigenvalues of large random matrices, written for mathematicians and others who study and use matrices but may not be accustomed to thinking about…
We study algebraic properties of full rank 1 algebras in a general framework and derive a method to verify if one such matrix polynomial sub-algebra is bispectral. We give two examples illustrating the method. In the first one, we consider…
In this paper we study the eigenvalues of the laplacian matrices of the cyclic graphs with one edge of weight $\alpha$ and the others of weight $1$. We denote by $n$ the order of the graph and suppose that $n$ tends to infinity. We notice…
In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…
We investigate the properties of positive definite and positive semi-definite symmetric matrices within the framework of symmetrized tropical algebra, an extension of tropical algebra adapted to ordered valued fields. We focus on the…
Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…
Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous…
We propose a new method for identifying and estimating the CP-factor models for matrix time series. Unlike the generalized eigenanalysis-based method of Chang et al. (2023) for which the convergence rates of the associated estimators may…
Let $f(x_1,...,x_k)$ be a polynomial over a field $K$. This paper considers such questions as the enumeration of the number of nonzero coefficients of $f$ or of the number of coefficients equal to $\alpha\in K^*$. For instance, if $K=\ff_q$…
The set of matrix tuples with invariant subspaces whose dimensions sum up to the dimension of the space, but which do not span the whole space form an algebraic hypersurface. We found the equation of this hypersurface. This generalizes…