The eigenvalues of the elliptic N-body Ruijsenaars operator are obtained by a dynamical version of the algebraic nested Bethe ansatz method. The result is derived by using the construction given in [1], where the Ruijsenaars operator was obtained as the transfer matrix associated to the symmetric power of the vector representation of the elliptic quantum group Eτ,γ(glN ).

The action of a subgroup G of automorphisms of a graph X is said to be 2 -transitive if it is vertexand edgebut not arc-transitive. In this case the graph X is said to be (G, 2)-transitive. In particular, X is 1 2 -transitive if it is (Aut X, 1 2)-transitive. The 2 -transitive action of G on X induces an orientation of the edges of X which is preserved by G. Let X have valency 4. An even length...

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 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">)...