Related papers: Determinants of Binomial-Related Circulant Matrice…

Let $\{a_k\}$ be a sequence of real numbers defined by an $m$th order linear homogenous recurrence relation. In this paper we obtain a determinant formula for the circulant matrix $A=circ(a_1, a_2, \cdots, a_n)$, providing a generalization…

Circulant matrices over finite fields and over commutative finite chain rings have been of interest due to their nice algebraic structures and wide applications. In many cases, such matrices over rings have a closed connection with diagonal…

We study the determinant of the pxp circulant matrix whose first row is (1,-x,0,...,0,-y,0,...,0), the -y being in position q+1. The coefficients of this polynomial are integers that count certain classes of permutations. We show that all…

Double circulant matrices are introduced and studied. A formula to compute the rank r of a double circulant matrix is exhibited; and it is shown that any consecutive r rows of the double circulant matrix are linearly independent. As a…

We describe algorithms for computing maximal determinants of binary circulant matrices of small orders. Here "binary matrix" means a matrix whose elements are drawn from $\{0,1\}$ or $\{-1,1\}$. We describe efficient parallel algorithms for…

In this paper, the determinants of $n\times n$ matrices over commutative finite chain rings and over commutative finite principal ideal rings are studied. The number of $n\times n$ matrices over a commutative finite chain ring ${R}$ of a…

The generalized sequence of numbers is defined by W_{n}=pW_{n-1}+qW_{n-2} with initial conditions W_{0}=a and W_{1}=b for a,b,p,q\inZ and n\geq2, respectively. Let W_{n}=circ(W_{1},W_{2},...,W_{n}). The aim of this paper is to establish…

We describe a class of matrices whose determinants are trivial to compute. A nice example of such a matrix is given by considering the symmetric matrix with entries {i+j choose i} (mod 2) in {0,1}, 0 <= i,j < n the binomial coefficients…

In this paper, firstly, we give the some fundamental properties of Van Der Laan numbers. After, we define the circulant matrices C(Z) which entries is third order linear recurrent sequence. In addition, we compute eigenvalues, spectral norm…

The determinant of an $N \times N$ circulant matrix $M = {\rm CIRC}[x_0, x_1, ..., x_{N-1}$] can be expanded in the form det$ ~M= \sum C_{a_0 a_1 ...a_{N-1}} x_{a_0} x_{a_1}...x_{a_{N-1}}$. By using the generating function of a restricted,…

This work presents closed formulas for determinant, permanent, inverse, and Drazin inverse of circulant matrices with two non-zero coefficients.

Using recurrence matrices, defined and described with some details, we study a few determinants related to evaluations of binomial coefficients on Dirichlet characters modulo 2, 4 and 8.

We study determinants of matrices whose entries are powers of Fibonacci numbers. We then extend the results to include entries that are powers of generalized Fibonacci numbers defined as a second-order linear recurrence relation. These…

This paper is intended to give closed formulae for binomial determinants with consecutive or almost consecutive rows or columns, as well as calculating the generator of left nullspaces defined by some binomial matrices. In the meantime, we…

We discuss several conjectures about the real-rootedness of polynomials whose coefficients are determinants of coefficients of a real-rooted polynomial. We also consider some questions about matrices generalizing totally positive matrices,…

In this paper, we present sufficient conditions to guarantee the invertibility of rational circulant matrices with any given size. These sufficient conditions consist of linear combinations of the entries in the first row with integer…

This article examines matrices whose entries are determined by recursive relations of the form $A_{i, j} = x A_{i, j-1} + y A_{i-1, j-1} + z A_{i-1, j}$, where $x, y, z$ are constants, and the initial conditions are defined along the first…

We evaluate determinants of "spiral" matrices, which are matrices in which entries are spiralling from the centre of the matrices towards the outside, with prescribed increments from one entry to the next depending on whether one moves…

We compute two parametric determinants in which rows and columns are indexed by compositions, where in one determinant the entries are products of binomial coefficients, while in the other the entries are products of powers. These results…

A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…