Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Determinants and inverses of circulant matrices with complex Fibonacci numbers
View through CrossRef
Abstract
Let ℱn = circ (︀F*1 , F*2, . . . , F*n︀ be the n×n circulant matrix associated with complex Fibonacci numbers
F*1, F*2, . . . , F*n. In the present paper we calculate the determinant of ℱn in terms of complex Fibonacci
numbers. Furthermore, we show that ℱn is invertible and obtain the entries of the inverse of ℱn in terms of
complex Fibonacci numbers.
Title: Determinants and inverses of circulant matrices with complex Fibonacci numbers
Description:
Abstract
Let ℱn = circ (︀F*1 , F*2, .
.
.
, F*n︀ be the n×n circulant matrix associated with complex Fibonacci numbers
F*1, F*2, .
.
.
, F*n.
In the present paper we calculate the determinant of ℱn in terms of complex Fibonacci
numbers.
Furthermore, we show that ℱn is invertible and obtain the entries of the inverse of ℱn in terms of
complex Fibonacci numbers.
Related Results
Inner-gMP and gMP-inner inverses
Inner-gMP and gMP-inner inverses
Solving some systems of operator equations, new kinds of generalized inverses are introduced. Since these new inverses can be expressed by inner and gMP inverses, they are called i...
Some Properties of the Fibonacci Sequence
Some Properties of the Fibonacci Sequence
The purposes of this paper are; (a) to develop a relationship between subscripts of the symbols of Fibonacci and Lucas numbers and the numbers themselves; (b) to develop relationsh...
On Matrices with Bidimensional Fibonacci Numbers
On Matrices with Bidimensional Fibonacci Numbers
Abstract
In this paper, the bidimensional extensions of the Fibonacci numbers are explored, along with a detailed examination of their properties, characteristics, a...
Some properties of Max-Plus Algebra and generalized inverses on 2x2 matrices integers modulo 3
Some properties of Max-Plus Algebra and generalized inverses on 2x2 matrices integers modulo 3
Abstract
The properties of Max Plus Algebra can be applied to the matrix. Furthermore, the generalized inverses in a matrix can also be related to this algebra. This...
Construction of Efficient MDS Matrices Based on Block Circulant Matrices for Lightweight Application
Construction of Efficient MDS Matrices Based on Block Circulant Matrices for Lightweight Application
Maximum distance separable (MDS) codes introduce MDS matrices which not only have applications in coding theory but also are of great importance in the design of block ciphers. It ...
Block-circulant with circulant-block preconditioners for two-dimensional spatial fractional diffusion equations
Block-circulant with circulant-block preconditioners for two-dimensional spatial fractional diffusion equations
Abstract
The implicit finite difference scheme with the shifted Grünwald formula for discretizing the two-dimensional spatial fractional diffusion equations can result in d...
Subespacios hiperinvariantes y característicos : una aproximación geométrica
Subespacios hiperinvariantes y característicos : una aproximación geométrica
The aim of this thesis is to study the hyperinvariant and characteristic subspaces of a matrix, or equivalently, of an endomorphism of a finite dimensional vector space. We restric...
Mòduls locals de sistemes dinàmics lineals amb coeficients constants
Mòduls locals de sistemes dinàmics lineals amb coeficients constants
La present memòria estudia l'estabilitat estructural de ternes de matrius. Es ben conegut que els sistemes dinàmic lineals amb coeficients constants poden venir definits per ternes...