Constructing New Matrices and Investigating Their Determinants

Abstract

Let λ = (λi)i ≥ 1, μ = (μi)i ≥ 1, ν = (νi)i ≥ 1, ω = (ωi)i ≥ 1 and ψ = (ψi)i ≥ 1 be given sequences, and let (ai,j)i,j ≥ 1 be the doubly indexed sequence given by the recurrence [Formula: see text](i ≥ 3, j ≥ 2), with various choices for the two first rows a1,j, a2,j and first column ai,1. Note that the coefficients depend on the row index only. In this article we study the principal minors of doubly indexed sequences (ai,j)i,j ≥ 1 for certain sequences and certain initial conditions. Moreover, let (bi,j)i,j ≥ 1 be the doubly indexed sequence given by the recurrence [Formula: see text] with various choices for the first row b1,j and first column bi,1. We also study the principal minors of doubly indexed sequence (bi,j)i,j ≥ 1.

Determinants of binomial-related circulant matrices

“…Determinants are known for their applications in matrix theory and linear algebra, e.g., determining the area of a triangle via Heron's formula in [9], solving linear systems using Cramer's rule in [3], and determining the singularity of a matrix. Therefore, properties matrices and determinants of matrices have been extensively studied (see [3], [12], and references therein). The determinants of circulant matrices have been studied (see, for example, [4], [8], [11], and [7]).…”

Determinants of matrices over commutative finite principal ideal rings

“…a matrix. Therefore, properties of matrices and determinants of matrices have been extensively studied (see [3], [12], and references therein). Especially, matrices over finite fields are interesting due to their rich algebraic structures and various applications.…”

“…Determinants are known for their applications in matrix theory and linear algebra, e.g., determining the area of a triangle via Heron's formula in [8], solving linear systems using Cramer's rule in [3], and determining the singularity of a matrix. Therefore, properties of matrices and determinants of matrices have been extensively studied (see [3], [12], and references therein). Especially, matrices over finite fields are interesting due to their rich algebraic structures and various applications.…”