Studying new generalizations of Max-Min matrices with a novel approach

Abstract

We consider new kinds of max and min matrices, [ a max (i,j) ]i,j≥1 and [ a min(i,j) ]i,j≥1 , as generalizations of the classical max and min matrices. Moreover, their reciprocal analogues for a given sequence {an} have been studied.We derive their LU and Cholesky decompositions and their inverse matrices as well as the LU -decompositions of their inverses. Some interesting corollaries will be presented.

The linear algebra of a generalized Tribonacci matrix

“…In [19], the authors give some properties of such matrices. The related results provide the alternative proofs for Theorem 2 and Theorem 5.…”

“…This method is used to simplify calculations, especially in solving a problem that is difficult to solve in its original form. Several authors are interested in matrix factorizations of some special matrices, see [1,2,7,18,19,27].…”

Some Properties of Generalized Frank Matrices

“…There are many matrices defined on maximum and minimum concepts. Some of them have been mentioned by Kılıç and Arıkan [5]. Also, they have introduced new generalizations of the classical Max and Min matrices and have derived their inverses, LU and Cholesky decompositions and their inverse matrices.…”