摘要
借助递推关系研究了广义m阶Fibonacci和Lucas数,在经典行列式定义的基础上,利用排列组合以及逆序数理论,给出了广义m阶Fibonacci和Lucas四元数矩阵的行列式的定义,基于Binet型公式以及范德蒙行列式的性质,探讨了广义m阶Fibonacci和Lucas四元数矩阵的行列式的计算,特别地,当m=2,3,4时,给出了Fibonacci和Lucas四元数矩阵的行列式的具体值。
The generalized m-step Fibonacci and Lucas numbers are studied by means of recursive relations.According to the classical definition of determinants,the determinants of generalized m-step Fibonacci and Lucas quaternion matrices are defined by the theory of permutation and combination and inverse number theory.Based on Binet formula and the properties of Vandermonde determinants,the determinants of generalized m-step Fibonacci and Lucas quaternion matrices are calculated.Specially,when m=2,3,4,the values of the determinants for Fibonacci and Lucas quaternion matrices are given.
作者
杨衍婷
YANG Yan-ting(School of Mathematics and Statistics,Xianyang Normal University,Xianyang Shaanxi,712000)
出处
《山西大同大学学报（自然科学版）》
2023年第4期32-35,48,共5页
Journal of Shanxi Datong University(Natural Science Edition)
基金
陕西省十四五教育科学规划课题[SGH22Y1441]
咸阳师范学院自然科学基金项目[XSYK20023]。
