Let k be a nonzero complex number. In this paper, we consider a k-circulant matrix whose first row is \((Q_{1},Q_{2},\ldots ,Q_{n})\), where \(Q_{n}\) is the nth Pell–Lucas number. The formulas for the eigenvalues of such matrix are obtained. Namely, the result which can be obtained from the result of Theorem 7. (Yazlik and Taskara, J Inequal Appl 2013:394, 2013) is improved. The obtained formulas for the eigenvalues of a k-circulant matrix involving the Pell–Lucas numbers show that the result of Theorem 8. (Jing, Li and Shen, WSEAS Trans Math 12(3):341-351, 2013) (i.e. Theorem 8. (Yazlik and Taskara 2013)) is not always applicable. The Euclidean norm of such matrix is determined. The upper and lower bounds for the spectral norm of a k-circulant matrix whose first row is \((Q_{1}^{-1},Q_{2}^{-1},\ldots ,Q_{n}^{-1})\) are also investigated. The obtained results are illustrated by examples. As a consequence of the previous results, the eigenvalues, the determinant, the Euclidean norm of a k-circulant matrix whose first row is \((q_{1},q_{2},\ldots ,q_{n})\), where \(q_{n}\) is the nth modified Pell number, are presented. Also, the upper and lower bounds for the spectral norm of a k-circulant matrix whose first row is \((q_{1}^{-1},q_{2}^{-1},\ldots ,q_{n}^{-1})\) are given

令k为非零复数。在本文中，我们考虑一个k循环矩阵，其第一行是\（（Q_ {1}，Q_ {2}，\ ldots，Q_ {n}）\），其中\（Q_ {n} \）是第n个佩尔–卢卡斯编号。获得了该矩阵特征值的公式。即，改进了可以从定理7的结果获得的结果。（Yazlik和Taskara，J Inequal Appl 2013：394，2013）。k的特征值的获得公式涉及佩尔-卢卡斯数的循环矩阵表明定理8的结果。（Jing，Li和Shen，WSEAS Trans Math 12（3）：341-351，2013）（即定理8。（Yazlik和Taskara 2013））并非总是适用。确定了这样的矩阵的欧几里得范数。的上限和下限要的光谱范ķ，其第一行是-circulant矩阵\（（Q_ {1} ^ { - 1}，Q_ {2} ^ { - 1}，\ ldots，Q_ {N} ^ {-1}）\）也会被调查。实例说明了所获得的结果。作为先前结果的结果，其第一行为\（（q_ {1}，q_ {2}，\ ldots，q_ {n}）\）的k-循环矩阵的特征值，行列式，欧几里得范数，其中\（q_ {n} \）是n给出了修改后的佩尔数。此外，对于一个的光谱范数的上界和下界ķ，其第一行是-circulant矩阵\（（Q_ {1} ^ { - 1}，Q_ {2} ^ { - 1}，\ ldots，Q_ {N } ^ { - 1}）\）中给出