a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$‎. ‎an $ntimes n$‎ ‎complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$)‎. ‎in this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...

This paper deals with the model reference tracking control problem of linear systems based on observer for Markov jump unknown transition rates. The main contributions are as follows: Firstly, we designed a descriptor given by matrix transformation. Then, law composed feedforward compensator and feedback was calculating variations observer. part can stabilize system. is complete parametric comp...

Based on the well-known Leverrier algorithm, a simple explicit solution to right factofization of a linear system is established. This solution is expressed by the controllability matrix of the given system and a symmetric operator matrix. Applications of this solution to a type of generalized Sylvester matrix equations and the problem of parametric eigenstructure assignment by state feedback a...

This is a collection of classical results about resultants and discriminants for polynomials, compiled mainly for my own use. All results are well-known 19th century mathematics, but I have not investigated the history, and no references are given. 1. Resultant Definition 1.1. Let f(x) = anx n + · · ·+ a0 and g(x) = bmx + · · ·+ b0 be two polynomials of degrees (at most) n and m, respectively, ...

‎In this paper‎, ‎an accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations is proposed‎. ‎The convergence analysis of the algorithm is investigated‎. ‎We show that the proposed algorithm converges to the exact solution for any initial value under certain assumptions‎. ‎Finally‎, ‎some numerical examples are given to demons...

This paper presents the non-linear generalization of a previous work on matrix differential models [1]. It focusses on the construction of approximate solutions of first-order matrix differential equations Y ′ (x) = f (x,Y (x)) using matrix-cubic splines. An estimation of the approximation error, an algorithm for its implementation and illustrative examples for Sylvester and Riccati matrix diff...