ON A SEQUENCE OF TRIDIAGONAL MATRICES WHOSE DETERMINANTS ARE FIBONACCI NUMBERS $F_{n+1}$

Trojovsk\'{y}, P.

doi:10.12732/ijpam.v102i3.10

Cited by 5 publications

(5 citation statements)

References 5 publications

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“…They showed that det(M α,β (k)) = F αk+β and det(T α,β (k)) = L αk+β , i.e., the determinants form subsequences of Fibonacci and Lucas numbers. For related results we refer to the works [35], [42] and [13].…”

Section: Fibonacci Numbers As Determinants Of Certain Special Matricesmentioning

confidence: 99%

Fibonacci Fervour in Linear Algebra and Quantum Information Theory

Chatterjee¹,

Singh²,

Sivakumar³

2018

Preprint

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Section: Fibonacci Numbers As Determinants Of Certain Special Matricesmentioning

confidence: 99%

Fibonacci Fervour in Linear Algebra and Quantum Information Theory

Chatterjee¹,

Singh²,

Sivakumar³

2018

Preprint

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“…He was 1 st European mathematician which work on Indian and Arabian mathematics. He gave a special type sequence [5,6,9] ‫ܨ‬ = ‫ܨ‬ ିଵ + ‫ܨ‬ ିଶ , ݊ ≥ 2 (1) With initial Term ‫ܨ‬ = 0 and ‫ܨ‬ ଵ = 1 Edouard Lucas dominated the field recursive series during the period 1878-1891 he was 1 st mathematician who applied Fibonacci's name for sequence (1) and it has been known as Fibonacci sequence since then. Lucas sequence given by [10,11,12].…”

Section: Introduction 11 Fibonacci Numbersmentioning

confidence: 99%

“Generating matrix for Generalized Fibonacci numbers and Fibonacci polynomials

Arya

Verma

2022

J. Phys.: Conf. Ser.

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Many researchers have been working on recurrence relation sequences of numbers and polynomials which are useful topic not only in mathematics but also in physics, economics and various applications in many other fields. There are many useful identities on recurrence relation sequence but there main problem to find any term of recurrence relation sequence we need to find previous all terms of recurrence relation sequence of numbers and polynomials. There were many important theorems obtained on recurrence relation sequences. In this paper we have given special identity for generalized Fibonacci sequence of number and Fibonacci sequence of polynomials. These identities are very useful to represent Fibonacci generalized sequence of numbers and Fibonacci sequence of polynomials in the form of matrix. Authors define a special formula in this paper by this we can find special representation of Fibonacci generalized sequence of numbers and Fibonacci sequence of polynomials in the form of matrix. So, we can say that this paper is generalization of property of Fibonacci sequence of number and Fibonacci sequence of polynomials

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“…Many authors derived the similar types of matrices which determinants or permanents are related to Fibonacci numbers or different kinds of their generalizations, e. g. k-generalized Fibonacci numbers, see [5], [7] [2], [6], [9] and [11]. Now we turn our attention to the relation of determinants of special tridiagonal matrices with Fibonacci numbers.…”

Section: Introductionmentioning

confidence: 99%

On Determinants of Tridiagonal Matrices With Alternating Pairs of 1' and -1' on the Diagonal Connected With Fibonacci Numbers

Trojovský¹

2016

Int. J. of Pure and Appl. Math.

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We will concentrate on some special tridiagonal matrices connected with Fibonacci numbers. In the previous paper we generalized one of the results in Strang's book, as we derived that determinants of some tridiagonal matrices with alternating 1 ′ s and −1 ′ s on the diagonal or the superdiagonal are connected with Fibonacci numbers. This paper is devoted to a generalization of that paper, we show determinants of tridiagonal matrices with alternating pairs of 1 ′ s and −1 ′ s on the diagonal are related to Fibonacci numbers too.

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ON A SEQUENCE OF TRIDIAGONAL MATRICES WHOSE DETERMINANTS ARE FIBONACCI NUMBERS $F_{n+1}$

Abstract: In this paper, we generalize two previous individual results on connection special tridiagonal matrices to Fibonacci numbers, as we found a sequence of tridiagonal matrices which are equal to Fibonacci numbers.

Cited by 5 publications

References 5 publications

Fibonacci Fervour in Linear Algebra and Quantum Information Theory

Fibonacci Fervour in Linear Algebra and Quantum Information Theory

“Generating matrix for Generalized Fibonacci numbers and Fibonacci polynomials

On Determinants of Tridiagonal Matrices With Alternating Pairs of 1' and -1' on the Diagonal Connected With Fibonacci Numbers

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