Vieta Matrix and its Determinant

Ufuk Kaya

paper

Vieta Matrix and its Determinant

arXiv:1809.07372

Abstract

In this paper, we define a matrix which we call Vieta matrix and calculate its determinant: $1 a_{2} + a_{3} + \dots + a_{n} a_{2} a_{3} + a_{2} a_{4} + \dots + a_{n - 1} a_{n} ⋮ a_{2} a_{3} \dots a_{n - 1} a_{n} 1 a_{1} + a_{3} + \dots + a_{n} a_{1} a_{3} + a_{1} a_{4} + \dots + a_{n - 1} a_{n} ⋮ a_{1} a_{3} \dots a_{n - 1} a_{n} \dots \dots \dots ⋱ \dots 1 a_{1} + a_{2} + \dots + a_{n - 1} a_{1} a_{2} + a_{1} a_{3} + \dots + a_{n - 2} a_{n - 1} ⋮ a_{1} a_{2} \dots a_{n - 2} a_{n - 1} .$