Convertible Subspaces of Hessenberg-Type Matrices

Abstract

Abstract:We describe subspaces of generalized Hessenberg matrices where the determinant is convertible into the permanent by affixing ± signs. An explicit characterization of convertible Hessenberg-type matrices is presented. We conclude that convertible matrices with the maximum number of nonzero entries can be reduced to a basic set.

On a recurrence for permanents of a sequence of 3-tridiagonal matrices

“…To prove [5,Conjecture 8] first da Fonseca in [8] showed that the permanent of the matrix T n (−1, 2x, 1), with respect to the fact, that the permanent of a square matrix equals the sum of the weights of all cycle-covers of its underlying directed graph. Then, he used a result on convertible matrices from his paper [10] (some generalizations can be found in [11]) to show that the permanent of matrix T (k) n (−1, 2x, 1) is equal to the determinant of the matrix T…”