Determinants and inverses of weighted Loeplitz and weighted Foeplitz matrices and their applications in data encryption

被引：10
|
作者：
Meng, Qingyan [1 ]
Zheng, Yanpeng [2 ]
Jiang, Zhaolin [1 ]
机构：
[1] Linyi Univ, Sch Math & Stat, Linyi 276000, Shandong, Peoples R China
[2] Linyi Univ, Sch Automat & Elect Engn, Linyi 276000, Shandong, Peoples R China
来源：
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2022年 / 68卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Weighted Loeplitz matrix; Weighted Foeplitz matrix; Lucas numbers; Fibonacci numbers; Determinant; Inverse; Data and image encryption; TOEPLITZ MATRICES; EIGENPAIRS; FIBONACCI;
D O I：
10.1007/s12190-022-01700-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the analytical determinants and inverses of n x n weighted Loeplitz and weighted Foeplitz matrices. We introduce the n x n weighted Loeplitz and weighted Foeplitz matrices and derive the analytical determinants and inverses of them by constructing the transformation matrices. Specifically, we can use the nth, (n + 1)st and (n + 2) th Fibonacci numbers to express the analytical inverse of the nxn weighted Loeplitz matrix which is sparse. We also present the analytical determiants and inverses of the n x n weighted Lankel and weighted Fankel matrices. Finally, we give two application examples of the main results in data and image encryption.
引用
收藏
页码：3999 / 4015
页数：17
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