THE MOORE-PENROSE INVERSE OF THE RECTANGULAR FIBONACCI MATRIX AND APPLICATIONS TO THE CRYPTOLOGY

被引：3

作者：

Aydinyuz, Sueleyman ^{[1
]}

Asci, Mustafa ^{[1
]}

机构：

[1] Pamukkale Univ, Fac Sci, Dept Math, TR-20160 Denizli, Turkiye

来源：

ADVANCES AND APPLICATIONS IN DISCRETE MATHEMATICS | 2023年 / 40卷 / 02期

关键词：

Fibonacci matrix; the Moore-Penrose generalized inverse; pseudo-inverse; encryption; cryptology;

D O I：

10.17654/0974165823066

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we define the general form of the Moore-Penrose inverse for the matrix whose elements are Fibonacci numbers. We examine the states of the matrix F e Mm ,n(C), where F is a rectangular Fibonacci matrix based on the values of m and n. In the second part of this study, we introduce a novel coding theory using the Moore-Penrose inverse of the rectangular Fibonacci matrix and provide illustrative examples. The rectangular Fibonacci matrix plays a crucial role in the construction of the coding algorithm. This coding method is referred to as the "coding theory on rectangular Fibonacci matrix."

引用

页码：195 / 211

页数：17

共 50 条

[11] Weighted Moore-Penrose inverse of a Boolean matrix
Bapat, RB
Jain, SK
Pati, S
LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 255 : 267 - 279
[12] Moore-Penrose inverse of an invertible infinite matrix
Sivakumar, KC
LINEAR & MULTILINEAR ALGEBRA, 2006, 54 (01): : 71 - 77
[13] The property of Moore-Penrose generalized inverse matrix
Tian Baoguang
Wang Nannan
Xia Lei
PROCEEDINGS OF THE THIRD INTERNATIONAL WORKSHOP ON MATRIX ANALYSIS AND APPLICATIONS, VOL 2, 2009, : 289 - 292
[14] The Moore-Penrose generalized inverse of a symmetric matrix
Puntanen, S
Styan, GPH
ECONOMETRIC THEORY, 1996, 12 (04) : 748 - 749
[15] Moore-Penrose inverse of a Euclidean distance matrix
Kurata, Hiroshi
Bapat, Ravindra B.
LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 472 : 106 - 117
[16] Weighted Moore-Penrose Inverse of a Fuzzy Matrix
Cheng, Shi-zhen
Li, Hong-xing
FUZZY INFORMATION AND ENGINEERING, VOLUME 2, 2009, 62 : 573 - +
[17] ON THE MOORE-PENROSE INVERSE OF A COMPLETELY SYMMETRICAL MATRIX
TRENKLER, G
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 1994, 49 (3-4) : 230 - 231
[18] FAST COMPUTING OF THE MOORE-PENROSE INVERSE MATRIX
Katsikis, Vasilios N.
Pappas, Dimitrios
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2008, 17 : 637 - 650
[19] The density of the Moore-Penrose inverse of a random matrix
Inst. of Actuar. Sci. and Economet., University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, Netherlands
Linear Algebra Its Appl, (123-126):
[20] Density of the Moore-Penrose inverse of a random matrix
Linear Algebra Its Appl, (123):

← 1 2 3 4 5 →