相关论文: Evaluating Two Determinants
After analyzing the 4x4 determinant of a matrix, a shortcut was obtained to find such a determinant. Similarly to the Sarrus method for 2x2 or 3x3 determinants, the method consists of laying 19 columns of size 4 each and adding and…
We define quantum determinants in Quantum Matrix Algebras, related to couples of compatible braidings following the scheme from [G]. We establish relations between these determinants and the so-called column-(row-)determinants, often used…
The use of quadratic residues to construct matrices with specific determinant values is a familiar problem with connections to many areas of mathematics and statistics. Our research has focused on using cubic residues to construct matrices…
This note collects several results on the capability of $p$-groups of class two and prime exponent. Among the new results, we settle the 4-generator case for this class.
The aim of this paper is to show that there exists a deterministic algorithm that can be applied to compute the factors of a polynomial of degree 2, defined over a finite field, given certain conditions.
We explore the possibility of using machine learning to identify interesting mathematical structures by using certain quantities that serve as fingerprints. In particular, we extract features from integer sequences using two empirical laws:…
We consider several extensions of the Maillet determinant studied by Malo, Turnbull, and Carlitz and Olson, and derive properties of the underlying matrices. In particular, we compute the eigenvectors and eigenvalues of these matrices,…
An exact expression for the determinant of the splitting matrix is derived: it allows us to analyze the asympotic behaviour needed to amend the large angles theorem proposed in Ann. Inst. H. Poincar\'e, B-60, 1, 1994. The asymptotic…
The goal of this work is twofold: (i) to provide a detailed analysis of some categories of inductive graded ring - a concept introduced in [DM98] in order to provide a solution of Marshall's signature conjecture in the algebraic theory of…
In this paper we introduce a class of determinants "of Hankel type". We use them to compute certain remarkable families of Drinfeld quasi-modular forms.
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…
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
The roles played by decision factors in making complex subject are decisions are characterized by how these factors affect the overall decision. Evidence that partially matches a factor is evaluated, and then effective computational rules…
Determinants and symmetric functions of the eigenvalues of matrices characterizing stochastic processes with indepedent increments. Relationships with Fibonacci numbers are derived.
Given positive integers $h, N$ satisfying $1 \leqslant h \leqslant 2N^2$, we define $T(h,N)$ to be the number of $2\times 2$ integer matrices with determinant equal to $h$ whose entries lie in $[-N,N]$. Our main result states that for any…
In this paper, a class of combinatorial identities is proved. A method is used which is based on the following rule: counting elements of a given set in two ways and making equal the obtained results. This rule is known as "counting in two…
In this paper, by the tools of circulant matrices and hyperelliptic curves over finite fields, we study some arithmetic properties of certain determinants involving the Legendre symbols and $k$-th residues.
From the matrix point of view, we use the recursion to discuss four combinatorial numbers in terms of the integer lattice paths, this is different from Andr\'a's method (Andra). We give four tables and matrices, and their relations, and…
We count with a smooth weight the number of $2 \times 2$ integer matrices with a fixed characteristic polynomial with a main term and an error term using bounds for sums of Weyl sums for quadratic roots.
A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by means of newly defined delayed matrix sine/cosine using the…