On the norms of r-circulant matrices with generalized Fibonacci numbers

In this paper, we obtain a generalization of [6, 8]. Firstly, we consider the so-called r-circulant matrices with generalized Fibonacci numbers and then found lower and upper bounds for the Euclidean and spectral norms of these matrices. Afterwards, we present some bounds for the spectral norms of Hadamard and Kronecker product of these matrices

A note on r-circulant matrices involving generalized Narayana numbers

In order to further connect structured matrices and integer sequences, r-circulant matrices involving the generalized Narayana numbers are considered. Estimates for spectral norms bounds of such matrices are presented and their eigenvalues are determined. Moreover, the conditions under which the circulant matrix and the skew circulant matrix involving generalized Narayana numbers are invertible are given. In particular, it is shown that every circulant matrix with Narayana numbers is necessarily invertible

The Determinants, Inverses, Norm, and Spread of Skew Circulant Type Matrices Involving Any Continuous Lucas Numbers

We consider the skew circulant and skew left circulant matrices with any continuous Lucas numbers. Firstly, we discuss the invertibility of the skew circulant matrices and present the determinant and the inverse matrices by constructing the transformation matrices. Furthermore, the invertibility of the skew left circulant matrices is also discussed. We obtain the determinants and the inverse matrices of the skew left circulant matrices by utilizing the relationship between skew left circulant matrices and skew circulant matrix, respectively. Finally, the four kinds of norms and bounds for the spread of these matrices are given, respectively