This paper presents a new type of circulant matrices. We call it the first and the last difference r-circulant matrix (FLDcircr matrix). We can verify that the linear operation, the matrix product and the inverse matrix of this type of matrices are still FLDcircr matrices. By constructing the basic FLDcircr matrix, we give the discriminance for FLDcircr matrices and the fast algorithm of the in...

In this paper, we consider a g-circulant matrixA 1(T), whose the first row entries are generalized Tribonacci numbers T(a)i. We give an explicit formula of spectral norm matrix. When g = 1, also present upper and lower bounds for spread 1-circulant matrix A1(T).

The computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. It is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of New-ton's method, but previous researchers have mentioned that some iter...

Let $d$ be an odd square-free integer and $\zeta_8$ a primitive $8$-th root of unity. The purpose this paper is to investigate the rank $2$-class group fields $L_d=\mathbb{Q}(\zeta_8,\sqrt{d})$.

Külshammer, Olsson and Robinson conjectured that a certain set of numbers determined the invariant factors of the `-Cartan matrix for Sn (equivalently, the invariant factors of the Cartan matrix for the Iwahori-Hecke algebra Hn(q), where q is a primitive `th root of unity). We call these invariant factors Cartan invariants. In a previous paper, the second author calculated these Cartan invarian...

This paper introduces a symbolic calculus to evaluate the output signals at the target line(s) of quantum computing subcircuits using controlled negations and controlled-Q gates, where Q represents the k-th root of [0 1; 1 0], the unitary matrix of NOT, and k is a power of two. The controlling signals are GF(2) expressions possibly including Boolean expressions. The method does not require oper...

The aim of this work is twofold: to unify, systematize and extend the known results of the analytical (i.e. formula-wise) counting of directed and undirected circulant graphs with a prime or, more generally, square-free number of vertices; to develop a general combinatorial framework for the counting of nonisomorphic circulant graphs with pk vertices, p odd prime, k 2. The general problem of co...

begin{abstract} the relations between the spectrum of the matrix $q+r$ and the spectra of the matrices $(gamma + delta)q+(alpha + beta)r-qr-rq$, $qr-rq$, $alpha beta r-qrq$, $alpha rqr-(qr)^{2}$, and $beta r-qr$ have been given on condition that the matrix $q+r$ is diagonalizable, where $q$, $r$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of order $...

In the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}A_{l}XB_{l}+overset{v} ‎{underset{s=1}{sum}}C_{s}widetilde{X}D_{s}=F$‎. ‎By this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎When the‎ ‎matrix equation is consistent over...