广义K阶Lucas数构成的矩阵的行列式  

On Determinants of Matrices with Order-k Generalized Lucas Numbers

作　　者：林洪娟[1] 马兴涛 

机构地区：[1]沈阳理工大学理学院,辽宁沈阳110159 [2]辽宁省水文水资源勘测局沈阳分局,辽宁沈阳110005

出　　处：《沈阳理工大学学报》2012年第4期57-59,共3页Journal of Shenyang Ligong University

摘　　要：用矩阵方程的形式表示了广义k阶Lucas递归序列,并利用广义k阶Lucas数的性质及矩阵的初等变换方法计算了由广义k阶Lucas数构成的矩阵的行列式.所定义的广义k阶Lucas序列中只要将系数c1取特定值,不论是否有n>0的条件都不改变由广义k阶Lucas数构成的矩阵的行列式,行列式的值只依赖于系数ck。The generalized order-k Lucas linear recurrence sequence is presented in matrix equation ; Furthermore, according to the properties of the generalized order-k Lucas numbers and elementary operations of matrix, the determinants of matrices obtained by the general- ized order-k Lucas numbers are computed. As long as the first coefficient of a specific val- ue, the determinants are not changed regardless of whether a condition n 〉 0 in the defini- tion of the generalized order-k Lucas sequence, they are only dependent on the last coeffi- cient.

关 键 词：广义k阶Lucas数 矩阵 行列式 

分 类 号：O151[理学—数学] O156[理学—基础数学]