Related papers: On the $\top$-Stein equation $X=AX^\top B+C$

The classical problem of computing a complete system of Stokes multipliers of a linear system of ODEs of rank one in terms of some connection coefficients of an associated hypergeometric system of ODEs, is solved with no genericness…

In this paper we will consider Rohde's general form of {1}-inverse of a matrix A. The necessary and sufficient condition for consistency of a linear system Ax=c will be represented. We will also be concerned with the minimal number of free…

This paper investigates the distributed computation of the well-known linear matrix equation in the form of $AXB = F$, with the matrices A, B, X, and F of appropriate dimensions, over multi-agent networks from an optimization perspective.…

We employ the M-P inverses and ranks of quaternion matrices to establish the necessary and sufficient conditions for solving a system of the dual quaternion matrix equations $(AX, XC) = (B, D)$, along with providing an expression for its…

We find all explicit involutive solutions $X \in \mathbb C^{n \times n}$ of the Yang-Baxter-like matrix equation $AXA=XAX$, where $A \in \mathbb C^{n \times n}$ is a given involutory matrix. The construction is algorithmic.

We derive closed formulas for the condition number of a linear function of the total least squares solution. Given an over determined linear system Ax=b, we show that this condition number can be computed using the singular values and the…

Let $X$ be a monoid scheme. We will show that the stalk at any point of $X$ defines a point of the topos $\Qc(X)$ of quasi-coherent sheaves over $X$. As it turns out, every topos point of $\Qc(X)$ is of this form if $X$ satisfies some…

The Gilbert-Steiner problem is a mass transportation problem, where the cost of the transportation depends on the network used to move the mass and it is proportional to a certain power of the "flow". In this paper, we introduce a new…

We derive several explicit formulae for finding infinitely many solutions of the equation $AXA=XAX$, when $A$ is singular. We start by splitting the equation into a couple of linear matrix equations and then show how the projectors…

This note further addresses the global optimization problem for max-plus linear systems considered in [Automatica 119 (2020) 109104]. Firstly, the operations between infinity elemens and real numbers involved in the formulas of solving…

Let us extend the pair of operations (max,+) over real numbers to matrices in the same way as in conventional linear algebra. We study integer images of max-plus linear mappings. The question whether Ax (in the max-plus algebra) is an…

Based on the geometric {\it Triangle Algorithm} for testing membership of a point in a convex set, we present a novel iterative algorithm for testing the solvability of a real linear system $Ax=b$, where $A$ is an $m \times n$ matrix of…

We study a class of overdetermined algebraic systems of equations. We prove that the number of distinct solutions equals to the maximal possible if and only if certain matrices are commuting and semisimple. This gives a characterization of…

We propose a new encoding of the first-order connection method as a Boolean satisfiability problem. The encoding eschews tree-like presentations of the connection method in favour of matrices, as we show that tree-like calculi have a number…

This paper proposes a new approach, grounded in Satisfiability Modulo Theories (SMT), to study the transient of a Max-Plus Linear (MPL) system, that is the number of steps leading to its periodic regime. Differently from state-of-the-art…

This paper investigates the conditions that guarantee unique solvability and unsolvability for the generalized absolute value equations (GAVE) given by $Ax - B \vert x \vert = b$. Further, these conditions are also valid to determine the…

We show that if $X$ is a Stein space and, if $\Omega \subset X$ is exhaustable by a sequence $\Omega_1 \subset \Omega_2 \subset \ldots \subset \Omega_n \subset \ldots$ of open Stein subsets of $X$, then $\Omega$ is Stein. This generalizes a…

It is shown that each positive map between matrix algebras is the sum of a maximal decomposable map and an atomic map which is both optimal and co-optimal. The result is analyzed in detail for the positive projection onto a spin factor.

Let $X$ be a finite set in $Z^d$. We consider the problem of optimizing linear function $f(x) = c^T x$ on $X$, where $c\in Z^d$ is an input vector. We call it a problem $X$. A problem $X$ is related with linear program $\max\limits_{x \in…

For the problem of solving Reynolds equation under natural boundary conditions, the corresponding hypothetical solution can be obtained by assuming the free boundary. If the solution satisfies natural boundary conditions, then the boundary…