According to the assumption that si = sj for i = j, the matrix (5) has an inverse and the system (2) and (4) can be solved. We denote by V the Vandermonde determinant of the matrix (5) and by Vk the Vandermonde determinant of order (n − 1) of the variables s1, . . . , sk−1, sk+1, . . . , sn. We also denote by Φ r the fundamental symmetric function of the r-th order of (n − 1) variables s1, . . ...

‎A full Nesterov-Todd (NT) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using Euclidean Jordan algebra‎. ‎Two types of‎ ‎full NT-steps are used‎, ‎feasibility steps and centering steps‎. ‎The‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

A matrix A = (aij) ∈ Rn×n is said to be symmetric and antipersymmetric matrix if aij = aji = −an−j+1,n−i+1 for all 1 ≤ i, j ≤ n. Peng gave the bisymmetric solutions of the matrix equation A1X1B1+A2X2B2+. . .+AlXlBl = C, where [X1, X2, . . . , Xl] is a real matrices group. Based on this work, an adjusted iterative method is proposed to find the symmetric and antipersymmetric solutions of the abo...

The concept of range symmetric matrix is introduced in Minkowski space m. Equivalent conditions for a matrix to be range symmetric are determined. The existence of the Minkowski inverse of a range symmetric matrix in m is discussed.

We study the problem of low-rank matrix completion for symmetric matrices. The minimum rank a generic partially specified depends only on location entries, and not their values, if complex entries are allowed. When required to be real, this is no longer case possible ranks called typical ranks. give combinatorial description patterns n×n matrices that have n as rank. Moreover, we describe exact...

We give a matrix factorization for the solution of the linear system Ax = f , when coefficient matrix A is a dense symmetric positive definite matrix. We call this factorization as "WW T factorization". The algorithm for this factorization is given. Existence and backward error analysis of the method are given. The WDWT factorization is also presented. When the coefficient matrix is a symmetric...

Abstract We show that if X n {X_{n}} is a variety of c × {c\times n} -matrices stable under the group Sym ⁡ ( stretchy="false">[ stretchy="false">] stretchy="false">)...