Related papers: A note on solutions of the matrix equation AXB=C
We provide an analytical framework for balanced realization model order reduction of linear control systems which depend on an unknown parameter. Besides recovering known results for the first order corrections, we obtain explicit novel…
We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called…
A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational…
In this paper we naturally obtain the values of the Barbero-Immirzi parameter as the solution of the simplicity constraints rather than setting it a priori. Particularly the Main theorem shows that if $\gamma = \pm i$ then the simplicity…
We consider approximating solutions to parameterized linear systems of the form $A(\mu_1,\mu_2) x(\mu_1,\mu_2) = b$. Here the matrix $A(\mu_1,\mu_2) \in \mathbb{R}^{n \times n}$ is nonsingular, large, and sparse and depends nonlinearly on…
Random matrices are widely used in sparse recovery problems, and the relevant properties of matrices with i.i.d. entries are well understood. The current paper discusses the recently introduced Restricted Eigenvalue (RE) condition, which is…
In this paper, we consider the iterative solution of linear algebraic equations under the condition that matrix-vector products with the coefficient matrix are computed only partially. At the same time, non-computed entries are set to…
Tensor networks have a gauge degree of freedom on the virtual degrees of freedom that are contracted. A canonical form is a choice of fixing this degree of freedom. For matrix product states, choosing a canonical form is a powerful tool,…
A sum of a large-dimensional random matrix polynomial and a fixed low-rank matrix polynomial is considered. The main assumption is that the resolvent of the random polynomial converges to some deterministic limit. A formula for the limit of…
The main goal of this article is to study the existence of a unique positive definite common solution to a pair of matrix equations of the form \begin{eqnarray*} X^r=Q_1 + \displaystyle \sum_{i=1}^{m} {A_i}^*F(X)A_i \mbox{ and } X^s=Q_2 +…
Given standard angular momentum and boost matrices, the commutation rules for vector and momentum matrices are solved. The resulting matrix components are displayed as detailed functions of spin with factors such as the square root of…
Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise…
This contribution presents two exponential stability criteria for linear systems with multiple pointwise and distributed delays. These results (necessary and sufficient conditions) are given in terms of the delay Lyapunov matrix and the…
In this paper, we propose an unconstrained framework for eigenvalue problems in both discrete and continuous settings. We begin our discussion to solve a generalized eigenvalue problem $A{\bf x} = \lambda B{\bf x}$ with two $N\times N$ real…
Boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices $K^{\pm}(\theta)$. For the six vertex model the general solution depending on…
A matrix $A$ is said to have $X$-simple image eigenspace if any eigenvector $x$ belonging to the interval $X=\{x\colon \underline{x}\leq x\leq\overline{x}\}$ is the unique solution of the system $A\otimes y=x$ in $X$. The main result of…
In this paper, we derive some necessary and sufficient solvability conditions for some systems of one sided coupled Sylvester-type real quaternion matrix equations in terms of ranks and generalized inverses of matrices. We also give the…
A few iterations of alternating least squares with a random starting point provably suffice to produce nearly optimal spectral- and Frobenius-norm accuracies of low-rank approximations to a matrix; iterating to convergence is unnecessary.…
In this paper the nonlinear matrix equation X-A^{*}X^{-p}A=Q with p>0 is investigated. We consider two cases of this equation: the case p>1 and the case 0<p<1. In the case p>1, a new sufficient condition for the existence of a unique…
We study a disordered system of interacting bosons described by the Bose-Hubbard Hamiltonian with random tunneling amplitudes. We derive the condition for the stability of the replica-symmetric solution for this model. Following the scheme…