EVALUATING SOME DETERMINANTS OF MATRICES WITH RECURSIVE ENTRIES

Title & Authors
EVALUATING SOME DETERMINANTS OF MATRICES WITH RECURSIVE ENTRIES
Moghaddamfar, Ali Reza; Salehy, Seyyed Navid; Salehy, Seyyed Nima;

Abstract
Let $\small{{\alpha}}$ = ($\small{{\alpha}_1,\;{\alpha}_2}$,...) and $\small{{\beta}}$ = ($\small{{\beta}_1,\;{\beta}_2}$,...) be two sequences with $\small{{\alpha}_1}$ = $\small{{\beta}_1}$ and k and n be natural numbers. We denote by $\small{A^{(k,{\pm})}_{{\alpha},{\beta}}(n)}$ the matrix of order n with coefficients $\small{{\alpha}_{i,j}}$ by setting $\small{{\alpha}_{1,i}}$ = $\small{{\alpha}_i,\;{\alpha}_{i,1}}$ = $\small{{\beta}_i}$ for 1 $\small{{\leq}}$ i $\small{{\leq}}$ n and $\small{{\alpha}_{i,j}=\{{\alpha}_{i-1,j-1}+{\alpha}_{i-1,j}\;if\;j{\equiv}}$2,3,4,..., k + 1 (mod 2k) $\small{\{{\alpha}_{i-1,j-1}-{\alpha}_{i-1,j}\;if\;j{\equiv}}$ k + 2,..., 2k + 1 (mod 2k) for 2 $\small{{\leq}}$ i, j $\small{{\leq}}$ n. The aim of this paper is to study the determinants of such matrices related to certain sequence $\small{{\alpha}}$ and $\small{{\beta}}$ and some natural numbers k.
Keywords
determinant;LU-factorization;recurrence relation;
Language
English
Cited by
1.
The determinants of matrices constructed by subdiagonal, main diagonal and superdiagonal, Lobachevskii Journal of Mathematics, 2010, 31, 3, 295
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