Related papers: Some results about the Equiangular Algorithm
This paper studies the concept of algorithmic equiresolution of a family of embedded varieties or ideals, which means a simultaneous resolution of such a family compatible with a given (suitable) algorithm of resolution in characteristic…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…
The diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling…
Tensor operations play an essential role in various fields of science and engineering, including multiway data analysis. In this study, we establish a few basic properties of the range and null space of a tensor using block circulant…
In this study, an algorithm for computing the inverse of periodic k banded matrices, which are needed for solving the differential equations by using the finite differences, the solution of partial differential equations and the solution of…
The alternate row and column scaling algorithm applied to a positive $n\times n$ matrix $A$ converges to a doubly stochastic matrix $S(A)$, sometimes called the \emph{Sinkhorn limit} of $A$. For every positive integer $n$, a two parameter…
A new algorithm is presented for computing a direct solution to a system of consistent linear equations. It produces a minimum norm particular solution, a generalized inverse (of type {124}), and a null space projection operator. In…
Using the theory of equitable decompositions it is possible to decompose a matrix $M$ appropriately associated with a given graph. The result is a collection of smaller matrices whose collective eigenvalues are the same as the eigenvalues…
A real square matrix is Perron-like if it has a real eigenvalue $s$, called the principal eigenvalue of the matrix, and $\mbox{Re}\,\mu<s$ for any other eigenvalue $\mu$. Nonnegative matrices and symmetric ones are typical examples of this…
Special orthogonal matrices with rational elements form the group SO(n,Q), where Q is the field of rational numbers. A theorem describing the structure of an arbitrary matrix from this group is proved. This theorem yields an algorithm for…
Eigenvalue and eigenpair backward errors are computed for matrix pencils arising in optimal control. In particular, formulas for backward errors are developed that are obtained under block-structure-preserving and…
In a polydiagonal subspace of the Euclidean space, certain components of the vectors are equal (synchrony) or opposite (anti-synchrony). Polydiagonal subspaces invariant under a matrix have many applications in graph theory and dynamical…
We develop several methods, based on the geometric relationship between the eigenspaces of a matrix and its adjoint, for determining whether a square matrix having distinct eigenvalues is unitarily equivalent to a complex symmetric matrix.…
A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent…
A straightforward model for deposition and evaporation on discrete cells of a finite array of any dimension leads to a matrix equation involving a Sylvester-Kac type matrix. The eigenvalues and eigenvectors of the general matrix are…
A procedure for counting the number of eigenvalues of a matrix in a region surrounded by a closed curve is presented. It is based on the application of the residual theorem. The quadrature is performed by evaluating the principal argument…
The question whether there exists an integral solution to the system of linear equations with non-negative constraints, $A\x = \b, \, \x \ge 0$, where $A \in \Z^{m\times n}$ and ${\mathbf b} \in \Z^m$, finds its applications in many areas,…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
Some puzzles which arise in matrix models with multiple cuts are presented. They are present in the smoothed eigenvalue correlators of these models. First a method is described to calculate smoothed eigenvalue correlators in random matrix…