A particular matrix with exponential form, its inversion and some norms

In this paper, we study a particular n x n matrix A = [a(kij]i,j=1)(n) and its Hadamard inverse A degrees((-1)), whose entire elements are exponential form a(k) = e(k/n) = e(2 pi ik/n), where k(ij )= min(i, j) + 1. We study determinants, leading principal minor and inversions of A, A degrees((-1)). Then the defined values of Euclidean norms, l(p) norms and spectral norms of these matrices are presented, rather than upper and lower bounds, which are different from other articles.

Automated summary

This paper studies a specific n x n matrix and its Hadamard inverse, which have elements in exponential form. The determinants, leading principal minor, and inversions of the matrices are examined. Additionally, the Euclidean norms, l(p) norms, and spectral norms of these matrices are defined rather than giving upper and lower bounds, differentiating it from other articles.