On the estimation of upper bound for solutions of perturbed discrete Lyapunov equations.
On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate
In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic...
On the -th roots of a complex matrix.
On the matrix equation over finite fields.
On the matrix negative Pell equation
Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) with d ∈ N for nonsingular , i=1,...,n.
On the parametric solution to the second-order Sylvester matrix equation .
On the reduction of a Hamiltonian matrix to Hamiltonian Schur form.
On the weight matrices of linear difference equations
On the Yang-Baxter-like matrix equation for rank-two matrices
Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.
One-sided complements and solutions of the equation in semirings.
One-sided simultaneous inequalities and sandwich theorems for diagonal similarity and diagonal equivalence of nonnegative matrices.