Power symmetric stochastic matrices

Properties of Central Symmetric X-Form Matrices

In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.

Ehrhart Series of Polytopes Related to Symmetric Doubly-Stochastic Matrices

In Ehrhart theory, the h∗-vector of a rational polytope often provides insights into properties of the polytope that may be otherwise obscured. As an example, the Birkhoff polytope, also known as the polytope of real doubly-stochastic matrices, has a unimodal h∗-vector, but when even small modifications are made to the polytope, the same property can be very difficult to prove. In this paper, w...

Power Indices of Trace Zero Symmetric Boolean Matrices

The power index of a square Boolean matrix A is the least integer d such that A is a linear combination of previous nonnegative powers of A. We determine the maximum power indices for the class of n × n primitive symmetric Boolean matrices of trace zero, the class of n × n irreducible nonprimitive symmetric Boolean matrices, and the class of n×n reducible symmetric Boolean matrices of trace zer...

Symmetric Error Structure in Stochastic DEA

Symmetric Quasidefinite Matrices

We say that a symmetric matrix K is quasi-definite if it has the form K = [ −E AT A F ] where E and F are symmetric positive definite matrices. Although such matrices are indefinite, we show that any symmetric permutation of a quasi-definite matrix yields a factorization LDLT . We apply this result to obtain a new approach for solving the symmetric indefinite systems arising in interior-point m...