This equation may be viewed as reducing the sum of n terms of the power sequence to a linear combination of the first r + 1 terms. Accordingly, there is an implicit assumption that n > v. Note that the matrix appearing as the middle factor on the right side of this equation is lower triangular. The zeros that should appear above the main diagonal have been omitted. The nonzero entries constitut...

In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and product based on Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the system of nonlinear algebraic equations w...

In this paper, the matrix equation AX + XB = C is considered, where the matrices A and B have sizes m × n and n × m, respectively, the size of the unknown X is n × m, and the operator (·) denotes either the transpose or the conjugate transpose of a matrix. In the first part of the paper, necessary and sufficient conditions for the existence and uniqueness of solutions are reviewed. These condit...

In this paper, the matrix equation AX + XB = C is considered, where the matrices A and B have sizes m × n and n × m, respectively, the size of the unknown X is n × m, and the operator (·) denotes either the transpose or the conjugate transpose of a matrix. In the first part of the paper, necessary and sufficient conditions for the existence and uniqueness of solutions are reviewed. These condit...

Abstract This study is devoted to some periodic matrix difference equations, through their associated product of companion matrices in blocks. Linear recursive sequences the algebra square blocks and generalized Cayley–Hamilton theorem are considered for working out results about powers Two algorithms computing finite built. Illustrative examples applications demonstrate effectiveness our appro...

Discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control and -control of Markovian jump linear systems are considered. First, the L_ equations that arise from the quadratic optimal control problem are studied. The matrix cost is only assumed to be hermitian. Conditions for existence of the maximal hermitian solution are derived in terms of the concept of mean sq...

the index of matrix a in cn.n is equivalent to the dimension of largest jor-dan block corresponding to the zero eigenvalue of a. in this paper, indicialequations and normal equations for solving inconsistent singular linear systemof equations are investigated.