Analytic inversion for a general case of certain classes of matrices

Abstract

The explicit inverse and determinant of a class of matrices are presented. The class under consideration is defined by 4n − 2 parameters, analytic expressions of which form the elements of the upper Hessenberg type inverse. These analytic expressions enable recursion formulae to be obtained, which reduce the arithmetic operations to O(n ²). The Hadamard product of two specific structures' matrices provides the class presented, special cases of which are already known classes of test matrices.

Keywords:

• Analytic inversion
• classes of matrices
• test matrices
• Hadamard product
• Hessenberg matrix

C.R. Categories:

• G.1.3
• F.2.1