Abstract The partition function of the Symmetric Matrix Ensemble is identified with $$\tau $$ ? -function a particular solution Pfaff Lattice. We show that, in case even power interactions, thermodynamic limit, corresponds to an integrable chain hydrodynamic type. prove that so obtained diagonalisable and adm...

For a given n by n matrix the ratio between the componentwise distance to the nearest singular matrix and the inverse of the optimal Bauer-Skeel condition number cannot be larger than (3 + 2 √ 2) · n. In this note a symmetric matrix is presented where the described ratio is equal to n for the choice of most interest in numerical computation, for relative perturbations of the individual matrix c...

In this paper, characterizations of secondary κkernel symmetric fuzzy matrices are obtained. Relation between sκkernel symmetric, skernel symmetric, κkernel symmetric and kernel symmetric matrices are discussed. Necessary and sufficient conditions are determined for a matrix to be sκkernel symmetric.