On the matrix equation X + ATX−1A = I

On the Matrix Equation Xa − Ax = X

We study the matrix equation XA − AX = X p in M n (K) for 1 < p < n. It is shown that every matrix solution X is nilpotent and that the generalized eigenspaces of A are X-invariant. For A being a full Jordan block we describe how to compute all matrix solutions. Combinatorial formulas for A m X ℓ , X ℓ A m and (AX) ℓ are given. The case p = 2 is a special case of the algebraic Riccati equation.

Steffensen method for solving nonlinear matrix equation $X+A^T X^{(-1)}A=Q$

In this article we study Steffensen method to solve nonlinear matrix equation $X+A^T X^{(-1)}A=Q$, when $A$ is a normal matrix. We establish some conditions that generate a sequence of positive denite matrices which converges to solution of this equation.

Perturbation Analysis for the Matrix Equation X − ∑

Homomorphisms on the monoid of fuzzy implications and the iterative functional equation I(x, I(x, y))=I(x, y)

Recently, Vemuri and Jayaram proposed a novel method of generating fuzzy implications, called the ~-composition, from a given pair of fuzzy implications (Vemuri and Jayaram, 2014). However, as with any generation process, the ~-composition does not always generate new fuzzy implications. In this work, we study the generative power of the ~-composition. Towards this end, we study some specific f...

On the solving of matrix equation of Sylvester type

A solution of two problems related to the matrix equation of Sylvester type is given. In the first problem, the procedures for linear matrix inequalities are used to construct the solution of this equation. In the second problem, when a matrix is given which is not a solution of this equation, it is required to find such solution of the original equation, which most accurately approximates the ...