The spectral norms of geometric circulant matrices with the generalized k-Horadam numbers.

In this paper, we use the algebra methods, the properties of the r-circulant matrix and the geometric circulant matrix to study the upper and lower bound estimate problems for the spectral norms of a geometric circulant matrix involving the generalized k-Horadam numbers, and we obtain some sharp estimations for them. We can also give a new estimation for the norms of a r-circulant matrix involving the generalized k-Horadam numbers.