In this paper, the eigenvalues of various non-Sylvester Hadamard matrices constructed by monomial permutation matrices are derived, which shows the relation between the eigenvalues of the newly constructed matrix and Sylvester Hadamard matrix. * The authors are with School of Electrical Engineering and Computer Science, Seoul National University, Seoul, Korea, ([email protected]). Paper No....

Fixed-order controller design for LTI-SISO polytopic systems is investigated using rank deficiency constraint on the controller Sylvester resultant matrix. It is shown that the non-convexity of fixed-order controller design problem can be contracted in a rank deficiency constraint on Sylvester resultant matrix of the controller. Then, an improved convex approximation of the rank deficiency cons...

Exponential time integrators are well-established discretization methods for semilinear systems of ordinary differential equations. These use ? ? functions, which matrix functions related to the exponential. This work introduces an algorithm speed up computation function action over vectors two-dimensional (2D) matrices expressed as a Kronecker sum. For that, we present auxiliary exponential-re...

James Joseph Sylvester coined the term “matrix” and contributed much to the early development of matrix theory. To mark the 200th anniversary of his birth I show how Sylvester’s work on matrices continues to influence applied mathematics today.

In this paper, we propose two new algorithms based on modified global Arnoldi algorithm for solving large Sylvester matrix equations AX + XB = C where A ∈ Rn×n, B ∈ Rs×s, X and C ∈ Rn×s. These algorithms are based on the global FOM and GMRES algorithms and we call them by Global FOM-SylvesterLike(GFSL) and Global GMRES-Sylvester-Like(GGSL) algorithms, respectively. Some theoretical results and ...

We provide necessary and sufficient conditions for the uniqueness of solution of the generalized Sylvester and ⋆-Sylvester equations, AXB − CXD = E and AXB+CX ⋆ D = E, respectively, where the matrix coefficients are allowed to be rectangular. These conditions generalize existing results for the same equations with square coefficients. Our characterization reveals unexpected constraints regardin...

A bent function is called self-dual if it is equal to its dual. It is called anti-self-dual if it is equal to the complement of its dual. A spectral characterization in terms of the Rayleigh quotient of the Sylvester Hadamard matrix is derived. Bounds on the Rayleigh quotient are given for Boolean functions in an odd number of variables. An efficient search algorithm based on the spectrum of th...

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...