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

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.