In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. This paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix S and a fuzzy triangular matrix T.

In this paper we consider a generalization to algebraic number fields of the classical Hermite constant γ n . For this constant we extend the well-known Minkowski bound and study the notion of extreme forms in this setting. Let us briefly recall the definition of Hermite’s constant. Let (a ij ) be a positive definite symmetric real n¬n matrix and let f(x " ,... ,x n ) ̄3 ij a ij x i x j be its a...

in this article the general non-symmetric parametric form of the incremental secant stiffness matrix for nonlinear analysis of solids have been investigated to present a semi analytical sensitivity analysis approach for geometric nonlinear shape optimization. to approach this aim the analytical formulas of secant stiffness matrix are presented. the models were validated and used to perform inve...

may be reduced to a single linear integral equation whose kernel is defined on a^x^a+n(b — a), a^s^a+n(b — a). Greggi§ considered a system of the form (1) and by use of the transformation introduced by Fredholm showed the form of the resolvent matrix for the system; for the symmetric system where Ku(x; s) =Kn(s; x) (i,j = \,2, ■ ■ ■ , n) he also stated theorems analogous to those proved by Schm...

in this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. this paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (st) decomposition. by this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix s and a fuzzy triangular matrix t.

A symmetric scaling of a square matrix A #0 is a matrix of the form XAX-' where X is a nonnegative, nonsingular, diagonal matrix having the same dimension of A. An asymmetric scaling of a rectangular matrix B # 0 is a matrix of the form XBY-' where X and Y"are nonnegative, nonsingular, diagonal matrices having appropriate dimensions. We consider two objectives in selecting a symmetric scaling o...

This note summarizes various derivations, formulas and computational algorithms relevant to the Fisher information matrix of Gaussian graphical models with respect to either an exponential parameterization (related to the information form) or the corresponding moment parameterization. 1 Gauss-Markov Models The probability density of a Gaussian random vector x ∈ R may be expressed in information...

It is known that any symmetric matrix M with entries in R[x] and which is positive semi-definite for any substitution of x ∈ R, has a Smith normal form whose diagonal coefficients are constant sign polynomials in R[x]. We generalize this result by considering a symmetric matrix M with entries in a formally real principal domain A, we assume that M is positive semi-definite for any ordering on A...