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k –step Fibonacci sequences and Fibonacci matrices.

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Title: k –step Fibonacci sequences and Fibonacci matrices.
Authors: Adam, Maria1, Assimakis, Nicholas2
Source: Journal of Discrete Mathematical Sciences & Cryptography. Aug2017, Vol. 20 Issue 5, p1183-1206. 24p.
Subjects: Fibonacci sequence, Mathematical bounds, Eigenvalues
Abstract: In this paper, the powers of the Fibonacci matrices are investigated and closed formulas for their entries are derived, related to the suitable terms of thek− step Fibonacci sequences in order to develop the properties of the irreducibility and primitivity of the Fibonacci matrices. Some bounds for the spectral radius and the modulus of the remaining eigenvalues of the Fibonacci matrices are presented. New formulas for computing of the odd and even terms of a special Fibonacci sequence are discussed, generalizing the Cassin’s and Sharpe’s formulas. [ABSTRACT FROM PUBLISHER]
Copyright of Journal of Discrete Mathematical Sciences & Cryptography is the property of Taru Publications and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 126349479
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: k –step Fibonacci sequences and Fibonacci matrices.
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  Data: <searchLink fieldCode="AR" term="%22Adam%2C+Maria%22">Adam, Maria</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Assimakis%2C+Nicholas%22">Assimakis, Nicholas</searchLink><relatesTo>2</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Discrete+Mathematical+Sciences+%26+Cryptography%22">Journal of Discrete Mathematical Sciences & Cryptography</searchLink>. Aug2017, Vol. 20 Issue 5, p1183-1206. 24p.
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  Data: <searchLink fieldCode="DE" term="%22Fibonacci+sequence%22">Fibonacci sequence</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+bounds%22">Mathematical bounds</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink>
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  Label: Abstract
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  Data: In this paper, the powers of the Fibonacci matrices are investigated and closed formulas for their entries are derived, related to the suitable terms of thek− step Fibonacci sequences in order to develop the properties of the irreducibility and primitivity of the Fibonacci matrices. Some bounds for the spectral radius and the modulus of the remaining eigenvalues of the Fibonacci matrices are presented. New formulas for computing of the odd and even terms of a special Fibonacci sequence are discussed, generalizing the Cassin’s and Sharpe’s formulas. [ABSTRACT FROM PUBLISHER]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Discrete Mathematical Sciences & Cryptography is the property of Taru Publications and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/09720529.2015.1104929
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      – Code: eng
        Text: English
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        PageCount: 24
        StartPage: 1183
    Subjects:
      – SubjectFull: Fibonacci sequence
        Type: general
      – SubjectFull: Mathematical bounds
        Type: general
      – SubjectFull: Eigenvalues
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      – TitleFull: k –step Fibonacci sequences and Fibonacci matrices.
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            NameFull: Adam, Maria
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            NameFull: Assimakis, Nicholas
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            – D: 01
              M: 08
              Text: Aug2017
              Type: published
              Y: 2017
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