Eigenvectors of Hessenberg Toeplitz matrices and a problem by Dai, Geary, and Kadanoff

Asymptotics of eigenvalues of large symmetric Toeplitz matrices with smooth simple-loop symbols

“…Note that the asymptotic structure of the eigenvectors in the case of n → ∞ is considered in the papers [28], [29], [30].…”

Cofactors and eigenvectors of banded Toeplitz matrices: Trench formulas via skew Schur polynomials

“…Let a 2 = 1, n = 7, ξ = (3, 6) and η = (3, 7). Then d = 2, m = 5, ρ = (1, 2, 4, 5, 7) and σ =(1,2,4,5,6). By striking out the rows ξ and the columns η in the Toeplitz matrix T 7 (a) we obtain the minordet(T 7 (a) ρ,σ ) = a 0 a −1 a −3 0 0 a 1 a 0 a −2 a −3 0 0 a 2 a 0 a −1 a −2 0 By Vieta's formulas the a k are expressed through e 2−k : det(T 7 (a) ρ,σ ) = −2 −e −1 −e 1 e 2 −e 3 e −4 −e −3 −e −1 e 0 −e Using (2.5), we have λ = (5 2 , 6 − 2, 3 − 1) = (5 2 , 4, 2) and µ = (7 − 2, 3 − 1) = (5, 2), then det(T n (a) ρ,σ ) = (−1) 10+19+18 s (5,5,4,2)/(5,2) = −s (5,4,2)/(2) .…”