Explicit inversion formulas for properly Hessenberg and Toeplitz-Hessenberg matrices

被引：2
|
作者：
Abderraman Marrero, Jesus [1 ]
机构：
[1] UPM Tech Univ Madrid, Dept Math Appl Informat Technol, Avda Complutense,30,Ciudad Univ, Madrid 28040, Spain
来源：
LINEAR & MULTILINEAR ALGEBRA | 2020年 / 68卷 / 06期
关键词：
Rajesh Pereira; Catalan numbers; Hessenbergian; inversion formula; nested sum; properly Hessenberg matrix; Toeplitz-Hessenberg matrix; REPRESENTATIONS; DETERMINANTS;
D O I：
10.1080/03081087.2018.1538312
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The nice inversion properties of Toeplitz-Hessenberg matrices from a Hessenbergian representation of Catalan's numbers encourage us to provide explicit inversion formulas (in terms of basic arithmetical operations involving entries from the original matrix) for the non-singular Toeplitz-Hessenberg matrices. Our approach is based on an elementary matrix inflation method, joint with the nested sums formulas. These explicit inversion formulas are then extended to apply to the entries of the inverse of every non-singular properly Hessenberg matrix.
引用
收藏
页码：1239 / 1256
页数：18
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