Abstract In this paper, we consider the k -Fibonacci and k -Lucas sequences {Fk,n}n∈N and {Lk,n}n∈N . Let A = Cr(Fk,0, Fk,1, · · · , Fk,n−1) and B = Cr(Lk,0, Lk,1, · · · , Lk,n−1) be r -circulant matrices. Afterwards, we give upper and lower bounds for the spectral norms of matrices A and B. In addition, we obtain some bounds for the spectral norms of Hadamard and Kronecker products of these ma...

We consider the Youden square formed by deleting one row of a v×v back-circulant Latin square and establish a critical set that contains a number of elements which is equal to v/4 (v even) or (v − 1)/4 (v odd). We show that this critical set is minimal, for v even.

([3]) and tvs(G) ≤ ⌈ 3n δ ⌉ + 1 ([1]). The exact values for some families of graphs are also known, e.g. the value of s(Cin(1, k), given in [2]. We prove that tvs(Cin(1, 2, . . . , k)) = n+2k 2k+1 , while s(Cin(1, 2, . . . , k)) = n+2k−1 2k . In order to do that, we split the graph Cin(1, 2, . . . , k) into segments and label each segment using 0, 1 and 2 in such a way that the weighted degrees...

We show that every weighing matrix of weight n invariant under a finite abelian group G can be generated from a subgroup H of G with |H| ≤ 2n−1. Furthermore, if n is an odd prime power and a proper circulant weighing matrix of weight n and order v exists, then v ≤ 2n−1. We also obtain a lower bound on the weight of group invariant matrices depending on the invariant factors of the underlying

This article identifies the general form of matrix power and trace an integer Special Form 3 × Complex Circulant matrix. The research begins to determine matrix, followed by determining proof is done using mathematical induction. final result this obtain A^n tr(A^n) for n integers in special complex

Partially due to the fact that the empirical data collected by devices with finite bandwidth often neither preserves the specified structure nor induces a certain desired rank, retrieving the nearest structured low rank approximation from a given data matrix becomes an imperative task in many applications. This paper investigates the case of approximating a given target matrix by a real-valued ...

This paper presents results on the memory capacity of a generalized feedback neural network using a circulant matrix. Children are capable of learning soon after birth which indicates that the neural networks of the brain have prior learnt capacity that is a consequence of the regular structures in the brain’s organization. Motivated by this idea, we consider the capacity of circulant matrices ...