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1.
In this paper, we present a new generalization of the Fibonacci quaternions that are emerged as a generalization of the best known quaternions in the literature, such as classical Fibonacci quaternions, Pell quaternions, k -Fibonacci quaternions. We give the generating function and the Binet formula for these quaternions. By using the Binet formula, we obtain some well-known results. Also, we correct some results in [3] and [4] which have been overlooked that the quaternion multiplication is non commutative.  相似文献   

2.
Starting from ideas given by Horadam in [5] , in this paper, we will define the split Fibonacci quaternion, the split Lucas quaternion and the split generalized Fibonacci quaternion. We used the well-known identities related to the Fibonacci and Lucas numbers to obtain the relations between the split Fibonacci, split Lucas and the split generalized Fibonacci quaternions. Moreover, we give Binet formulas and Cassini identities for these quaternions.  相似文献   

3.
In this paper, we investigate the Fibonacci and Lucas quaternions. We give the generating functions and Binet formulas for these quaternions. Moreover, we derive some sums formulas for them.  相似文献   

4.
In this paper, we introduce 8×8 real matrix representations of complex split quaternions. Then, the relations between real matrix representations of split and complex split quaternions are stated. Moreover, we investigate some linear split and complex split quaternionic equations with split Fibonacci and complex split Fibonacci quaternion coefficients. Finally, we also give some numerical examples as applications of real matrix representation of complex split quaternions.  相似文献   

5.
Starting from known results, due to Y. Tian in [5], referring to the real matrix representations of the real quaternions, in this paper we will investigate the left and right real matrix representations for the complex quaternions and we will give some examples in the special case of the complex Fibonacci quaternions.  相似文献   

6.
In this paper, we give a generalization of the Fibonacci and Lucas quaternions. We obtain the Binet formulas, generating functions, and some certain identities for these quaternions which include generalizations of some results of Halici.  相似文献   

7.
In this paper, the Fibonacci generalized quaternions are introduced. We use the well-known identities related to the Fibonacci and Lucas numbers to obtain the relations regarding these quaternions. Furthermore, the Fibonacci generalized quaternions are classified by considering the special cases of quaternionic units.  相似文献   

8.
In this paper, we investigate some properties of generalized Fibonacci quaternions and Fibonacci-Narayana quaternions in a generalized quaternion algebra.  相似文献   

9.
In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their fundamental matrices. After that we investigate commutative quaternion matrices using properties of complex matrices. Then we define the complex adjoint matrix of commutative quaternion matrices and give some of their properties.  相似文献   

10.
讨论了四元数中的真半范数,并给出了它的一般形式,它适合核维数分别为1,2,3的情形,推广了复数域中的真半范数的一般形式,给出了一个较好的结果.  相似文献   

11.
The integer split quaternions form a noncommutative algebra over ?. We describe the prime and maximal spectrum of the integer split quaternions and investigate integer-valued polynomials over this ring. We prove that the set of such polynomials forms a ring, and proceed to study its prime and maximal ideals. In particular we completely classify the primes above 0, we obtain partial characterizations of primes above odd prime integers, and we give sufficient conditions for building maximal ideals above 2.  相似文献   

12.
In the present paper, we give a new family of k-Fibonacci numbers and establish some properties of the relation to the ordinary Fibonacci numbers. Furthermore, we describe the recurrence relations and the generating functions of the new family for k=2 and k=3, and presents a few identity formulas for the family and the ordinary Fibonacci numbers.  相似文献   

13.
正定自共轭四元数矩阵的均值   总被引:4,自引:0,他引:4  
庄瓦金 《数学研究》1996,29(3):65-69
本文引进了两个正定自共轭四元数矩阵的算术均值,几何均值,调和均值三概念,给出了正定自共轭四元数矩阵的算术-几何-调和均值不等式,得到了正定自共轭四元数矩阵的几何均值的一个最大性质及其相关的某些性质.  相似文献   

14.
利用非数学归纳法,以及广义Fibonacci数的性质,得到了广义Fibonacci数的一些求和公式.  相似文献   

15.
本文给出了具有实谱值的四元数矩阵的定义,得到了一些具有实谱值的四元数矩阵的谱值不等式,这些不等式只涉及到了四元数矩阵的迹的实部和它的平方的迹的实部。  相似文献   

16.
In this paper, using the method of Laplace expansion to evaluate the determinant tridiagonal matrices, we construct a kind of determinants to give new proof of the Fibonacci identities.  相似文献   

17.
给出了计算一种三对角矩阵的特征值和特征向量的公式.利用矩阵的特征值理论证明了一些三角恒等式,特别是一些与Fibonacci数和第二类Chebyshev多项式有关的三角恒等式.  相似文献   

18.
四元数的复数形式及其在6R机器人反解中的应用   总被引:1,自引:0,他引:1  
把四元数应用于平面旋转的特殊情况,并把旋转角度的正弦、余弦改写为复指数形式,导出平面四元数的两个复数形式的基.利用这两个基可以把表示三维变换的四元数和对偶四元数改造为复数形式,得到复数形式四元数的4个基和复数形式对偶四元数的8个基,以及它们之间乘法运算的运算法则.通过把它们应用到空间$6R$机器人的位移反解问题,证明了Dixon结式展开后的次数为16次,而不是形式上的24次,并且得到单变量的16次方程.  相似文献   

19.
In this paper, we describe a simple representation of a circular arc in the space using quaternions. Using this representation, we obtain a subdivision of the arc, describe circular splines, and give a few applications with circular surfaces. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 2, pp. 298–310, April–June, 2006.  相似文献   

20.
In this short note, we give a factorization of the Pascal matrix. This result was apparently missed by Lee et al. [Some combinatorial identities via Fibonacci numbers, Discrete Appl. Math. 130 (2003) 527-534].  相似文献   

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