A new numerical procedure is proposed to solve the symmetric matrix polynomial equation A T (?s)X(s) + X T (?s)A(s) = 2B(s) that is frequently encountered in control and signal processing. It is based on interpolation and takes fully advantage of symmetry of the equation by reducing the original problem dimension. The algorithm is more eecient and more general than older methods and, namely, it...

For problems of linear control system synthesis, an apparatus of polynomial equations (for single-variable case) and of matrix polynomial equations (for multivariable case) was successfully developed in recent times, cf. [1]. In connection with quadratic criteria, we are led to equations of special type, containing an operation of conjugation ah-* a* representing a(s) i-> a( — s) for continuous...

The new symmetric cipher S-box construction based on matrix power function is presented. The matrix consisting of plain data bit strings is combined with three round key matrices using arithmetical addition and exponent operations. The matrix power means the matrix powered by other matrix. The left and right side matrix powers are introduced. This operation is linked with two sound one-way func...

A monic quadratic Hermitian matrix polynomial L(λ) can be factorized into a product of two linear matrix polynomials, say L(λ) = (Iλ−S)(Iλ−A). For the inverse problem of finding a quadratic matrix polynomial with prescribed spectral data (eigenvalues and eigenvectors) it is natural to prescribe a right solvent A and then determine compatible left solvents S. This problem is explored in the pres...

In the present paper we consider Dirichlet problem for second order differential operator E=?(A?), where A is a matrix with complex valued L? entries. We introduce concept of dissipativity E respect to given function ?:R+?R+. Under assumption that ImA symmetric, prove condition |s??(s)| |?ImA(x)?,??| ?2?(s)[s?(s)]? ?ReA(x)?,?? (for almost every x???RN and any s>0, ??RN) necessary sufficient fun...

In this note we consider completions of n×n symmetric (0,−1)-matrices to symmetric alternating sign matrices by replacing certain 0s with +1s. In particular, we prove that any n×n symmetric (0,−1)-matrix that can be completed to an alternating sign matrix by replacing some 0s with +1s can be completed to a symmetric alternating sign matrix. Similarly, any n × n symmetric (0,+1)-matrix that can ...

Abstract Williamson’s theorem states that for any $2n \times 2n$ real positive definite matrix A , there exists a symplectic S such $S^TAS=D \oplus D$ where D is an $n\times n$ diagonal with entries known as the eigenvalues of . Let H be symmetric perturbed $A+H$ also definite. In this paper, we show $\tilde {S}$ diagonalizing in form {S}=S Q+\mathcal {O}(\|H\|)$ Q well orthogonal matrix. Moreo...