Tensor Generalizations of the Fibonacci Matrix

Matthew He; Z. B. Hu; Sergey V. Petoukhov

doi:10.1007/978-3-030-39216-1_32

Tensor Generalizations of the Fibonacci Matrix

Matthew He
, Z. B. Hu
, Sergey V. Petoukhov

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The Fibonacci matrix [1, 1; 1, 0] is well known in the wide theme of Fibonacci numbers and their applications in various fields of mathematics, computer technologies and informatics, economics and biology. The article describes results of generalizations of the Fibonacci (2*2)-matrix on the basis of the tensor (Kronecker) product of matrices and also some features of Fibonacci-like (2ⁿ*2ⁿ)-matrices received in the result of such generalization. The main property of these considered matrices is that their exponentiation in integer powers k generates matrices, all entries of which are Fibonacci numbers with the same common factor 2 ^k−1.

Original language	English
Title of host publication	Advances in Intelligent Systems, Computer Science and Digital Economics, CSDEIS 2019
Editors	Zhengbing Hu, Sergey Petoukhov, Matthew He
Publisher	Springer
Pages	356-363
Number of pages	8
ISBN (Print)	9783030392154
DOIs	https://doi.org/10.1007/978-3-030-39216-1_32
State	Published - 2020
Event	International Symposium on Computer Science, Digital Economy and Intelligent Systems, CSDEIS 2019 - Moscow, Russian Federation Duration: Oct 4 2019 → Oct 6 2019

Publication series

Name	Advances in Intelligent Systems and Computing
Volume	1127 AISC
ISSN (Print)	2194-5357
ISSN (Electronic)	2194-5365

Conference

Conference	International Symposium on Computer Science, Digital Economy and Intelligent Systems, CSDEIS 2019
Country/Territory	Russian Federation
City	Moscow
Period	10/4/19 → 10/6/19

Bibliographical note

Publisher Copyright:
© 2020, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.

ASJC Scopus Subject Areas

Control and Systems Engineering
General Computer Science

Keywords

Eigenvalues
Fibonacci matrix
Fibonacci numbers
Phyllotaxis laws
Tensor product

Access to Document

10.1007/978-3-030-39216-1_32

Cite this

Tensor Generalizations of the Fibonacci Matrix. / He, Matthew; Hu, Z. B.; Petoukhov, Sergey V.
Advances in Intelligent Systems, Computer Science and Digital Economics, CSDEIS 2019. ed. / Zhengbing Hu; Sergey Petoukhov; Matthew He. Springer, 2020. p. 356-363 (Advances in Intelligent Systems and Computing; Vol. 1127 AISC).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

He, M, Hu, ZB & Petoukhov, SV 2020, Tensor Generalizations of the Fibonacci Matrix. in Z Hu, S Petoukhov & M He (eds), Advances in Intelligent Systems, Computer Science and Digital Economics, CSDEIS 2019. Advances in Intelligent Systems and Computing, vol. 1127 AISC, Springer, pp. 356-363, International Symposium on Computer Science, Digital Economy and Intelligent Systems, CSDEIS 2019, Moscow, Russian Federation, 10/4/19. https://doi.org/10.1007/978-3-030-39216-1_32

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keywords = "Eigenvalues, Fibonacci matrix, Fibonacci numbers, Phyllotaxis laws, Tensor product",

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Tensor Generalizations of the Fibonacci Matrix

Abstract

Publication series

Conference

Bibliographical note

ASJC Scopus Subject Areas

Keywords

Access to Document

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Cite this