A Generalization of a Class of Matrices : Analytic Inverse and Determinant

Abstract EN

The aim of this paper is to present the structure of a class of matrices that enables explicit inverse to be obtained.

Starting from an already known class of matrices, we construct a Hadamard product that derives the class under consideration.

The latter are defined by 4n−2 parameters, analytic expressions of which provide the elements of the lower Hessenberg form inverse.

Recursion formulae of these expressions reduce the arithmetic operations in evaluating the inverse to O(n2).