A matrix S ∈ C2m×2m is symplectic if SJS∗ = J , where J = [ 0 −Im Im 0 ] . Symplectic matrices play an important role in the analysis and numerical solution of matrix problems involving the indefinite inner product x∗(iJ)y. In this paper we provide several matrix factorizations related to symplectic matrices. We introduce a singular value-like decomposition B = QDS−1 for any real matrix B ∈ Rn×...

This paper is concerned with the approximation of the effective conductivity σ(A,μ) associated to an elliptic operator ∇xA(x, η)∇x where for x ∈ R , d ≥ 1, A(x, η) is a bounded elliptic random symmetric d×d matrix and η takes value in an ergodic probability space (X,μ). Writing A(x, η) the periodization of A(x, η) on the torus T d N of dimension d and side N we prove that for μ-almost all η lim...

in this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where a~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisti...

This paper is concerned with the approximation of the effective conductivity σ(A,μ) associated to an elliptic operator ∇xA(x, η)∇x where for x ∈ Rd, d ≥ 1, A(x, η) is a bounded elliptic random symmetric d× d matrix and η takes value in an ergodic probability space (X,μ). Writing AN (x, η) the periodization of A(x, η) on the torus T d N of dimension d and side N we prove that for μ-almost all η ...

The force regulation and inevitable positional inaccuracy of traditional control system can be compensated by the compliance/stiffness mechanism. The compliance/stiffness of a robotic mechanism is usually modeled by a 6 by 6 symmetric positive definite matrix at an equilibrium point using screw theory. When an external wrench is exerted on the mechanism and the mechanism moves away from its equ...

Three algorithms providing rigourous bounds for the eigenvalues of a real matrix are presented. The first is an implementation of the bisection algorithm for a symmetric tridiagonal matrix using IEEE floating-point arithmetic. The two others use interval arithmetic with directed rounding and are deduced from the Jacobi method for a symmetric matrix and the Jacobi-like method of Eberlein for an ...

Multiple symmetric lipomatosis (also known as Madelung's disease, Launois-Bensaude syndrome or benign symmetric lipomatosis) is a rare disease, the etiology of which is unknown. Multiple, symmetric, non-encapsulated lipomatous masses on the face, neck, upper arms, and upper trunk are typical in most cases. Five out of the 200 cases reported in the literature were the distal form of the disease;...

We establish two sufficient conditions for the stability of a P -matrix. First, we show that a P -matrix is positive stable if its skew-symmetric component is sufficiently smaller (in matrix norm) than its symmetric component. This result generalizes the fact that symmetric P -matrices are positive stable, and is analogous to a result by Carlson which shows that sign symmetric P -matrices are p...

The spectral radius p(A) of the adjacency matrix A of a graph G with e edges satisfiesp(A)<i(-l+~~).Equalityoccnrsifandonlyif e= i andGisa disjoint union of the complete graph K, and isolated vertices. 0 Let A be a symmetric (0,l) matrix with zero trace (i.e., the adjacency matrix of a graph G). Let the number of l’s of A be 2 (k) (so G has (i) edges). R. A. Brualdi and A. J. Hoffmann [l, Theor...