The purpose of this paper is to show how the problem of finding the zeros of unilateral n-order quaternionic polynomials can be solved by determining the eigenvectors of the corresponding companion matrix. This approach, probably superfluous in the case of quadratic equations for which a closed formula can be given, becomes truly useful for (unilateral) n-order polynomials. To understand the st...

A full-rank lattice L in R is a discrete subgroup of R which is the set of all integer linear combinations of n-linearly independent vectors, say b1, · · · ,bn i.e., L = { ∑n i=1 zibi | z1, · · · , zn ∈ Z}. The matrix B = [b1, · · · ,bn] is called the basis of the lattice and the matrix Q = B′B is called a Gram matrix of the lattice. A lattice is integral if its Gram matrix has only integer ent...

begin{abstract} the relations between the spectrum of the matrix $q+r$ and the spectra of the matrices $(gamma + delta)q+(alpha + beta)r-qr-rq$, $qr-rq$, $alpha beta r-qrq$, $alpha rqr-(qr)^{2}$, and $beta r-qr$ have been given on condition that the matrix $q+r$ is diagonalizable, where $q$, $r$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of order $...

We study the nonsymmetric algebraic Riccati equation whose four coefficient matrices are the blocks of a nonsingular M -matrix or an irreducible singular M -matrix M . The solution of practical interest is the minimal nonnegative solution. We show that Newton’s method with zero initial guess can be used to find this solution without any further assumptions. We also present a qualitative perturb...

This paper discusses an Interval Quadratic Programming (IQP) problem, where the constraints coefficients and the right-hand sides are represented by interval data. First, the focus is on a common method for solving Interval Linear Programming problem. Then the idea is extended to the IQP problem. Based on this method each IQP problem is reduced to two classical Quadratic Programming (QP) proble...

begin{abstract} The relations between the spectrum of the matrix $Q+R$ and the spectra of the matrices $(gamma + delta)Q+(alpha + beta)R-QR-RQ$, $QR-RQ$, $alpha beta R-QRQ$, $alpha RQR-(QR)^{2}$, and $beta R-QR$ have been given on condition that the matrix $Q+R$ is diagonalizable, where $Q$, $R$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of ord...

won{gil park [won{gil park, j. math. anal. appl., 376 (1) (2011) 193{202] proved the hyers{ulam stability of the cauchy functional equation, the jensen functional equation and the quadraticfunctional equation in 2{banach spaces. one can easily see that all results of this paper are incorrect.hence the control functions in all theorems of this paper are not correct. in this paper, we correctthes...

In this paper, we consider Newton’s method and Bernoulli’s method for a quadratic matrix equation arising from an overdamped vibrating system. By introducing M-matrix to this equation, we provide a sufficient condition for the existence of the primary solution. Moreover, we show that Newton’s method and Bernoulli’s method with an initial zero matrix converge to the primary solvent under the pro...