Some determinantal considerations for pentadiagonal matrices

A Study on the Determinants of some Hessenberg Toeplitz Bohemians

“…Except as the speci…c statement, we follow the notations as in [22], all mentioned elements are 1s, all the unmentioned elements are zeros.…”

“…For the determinant of 2-tridiagonal Toeplitz matrix, which has been studied in [22], [15], [20], [12]. Expanding the determinant by the last row and last column, we obtain a recurrence relation jT (2) n j = jT…”

“…Using the above recurrence relations, we can compute the …rst some terms of two sequences as the followings As the result of 7-term recurrence relation [24], [22], we know a recurrence relation jP n j = jP n 1 j + jP n 5 j jP n 6 j. By the software Maple, we obtain jP n j = 1; if n 0; 1 (mod 5)…”

“…Recently Andelic and Fonseca [22] considered how to evaluate the determinants of the pentadiagonal Toeplitz matrix and proposed a research problem: "Find the determinant of a pentadiagonal Toeplitz matrix, where the four subdiagonals are not necessarily immediately below (two) and above (two) the main diagonal or are not consecutive. "They proposed two conjectures in the cases of pentadiagonal matrices containing one or two entries in the second subdiagonal above the main diagonal.…”

Analytic determinants and inverses of Toeplitz and Hankel tridiagonal matrices with perturbed columns

“…In addition, Eigenpairs, determinants and inverses of the tridiagonal matrices, anti-tridiagonal Hankel matrices, pentadiagonal matrices and cyclic pentadiagonal matrices with Toeplitz structure have been studied in [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The determinant and inversion of A(c , an; d k , a k , c k ; a , cn) have been studied extensively and found with simple and analytic expression (see [24][25][26]).…”