A matrix P ∈ Rn×n is said to be a symmetric orthogonal matrix if P = P T = P−1. A matrix A ∈ Rn×n is said to be generalized centro-symmetric (generalized central anti-symmetric )with respect to P , if A = PAP (A = −PAP ). In this paper, an iterative method is constructed to solve the generalized centrosymmetric solutions of a linear matrix equation AXB + CY D = E, with real pair matrices X and ...

in this paper, a new method based on parametric form for approximate solu-tion of fuzzy linear matrix equations (flmes) of the form ax = b; where ais a crisp matrix, b is a fuzzy number matrix and the unknown matrix x one,is presented. then a numerical example is presented to illustrate the proposedmodel.

Abstract. Let A be an n by n symmetric matrix with real entries. Using the l1-norm for vectors and letting S 1 = {x ∈ R|||x||1 = 1, x ≥ 0}, the matrix A is said to be interior if the quadratic form x Ax achieves its minimum on S 1 in the interior. Necessary and sufficient conditions are provided for a matrix to be interior. A copositive matrix is referred to as being exceptional if it is not th...

In this paper we present a formula for the calculation of the integrals of the form ∫ S u∗Xuν(du), where S is the unit sphere in R , X is a positive semi-definite symmetric matrix, and ν is a surface measure generated by a Gaussian measure μ. The solution has the form trace(XZ), with the explicit procedure for the calculation of the matrix Z which does not depend on X. AMS subject classificatio...

We provide necessary and sufficient conditions for the matrix equation $$X^\top A X=B$$ to be consistent when B is a symmetric matrix, all matrices with few exceptions. The A, B, X (unknown) are complex entries. first see that we can restrict ourselves case where given in canonical form congruence and, then, address such form. characterization strongly depends on of A. problem solve equivalent ...

Let A be an n by n symmetric matrix with real entries. Using the l1-norm for vectors and letting S 1 = {x ∈ Rn|||x||1 = 1, x ≥ 0}, the matrix A is said to be interior if the quadratic form xT Ax achieves its minimum on S 1 in the interior. Necessary and sufficient conditions are provided for a matrix to be interior. A copositive matrix is referred to as being exceptional if it is not the sum of...

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...

We consider optimization problems of the following type: min{tr(CX) : A(X) = B,X positive semidefinite}. Here, tr(·) denotes the trace operator, C and X are symmetric n× n matrices, B is a symmetric m ×m matrix and A(·) denotes a linear operator. Such problems are called semidefinite programs and have recently become the object of considerable interest due to important connections with max-min ...

The vacuum solution ds 2 = dx 2 + x 2 dy 2 + 2 dz dt + ln x dt 2 of the Einstein gravitational field equation follows from the general ansatz ds 2 = dx 2 + g αβ (x) dx α dx β but fails to follow from it if the symmetric matrix g αβ (x) is assumed to be in diagonal form.