Exact Determinants and Inverses of Skew Symmetric Generalized Loeplitz Matrices

Main Article Content

Xiaoting Chen


In this paper, exact determinants and inverses of skew symmetric generalized Loeplitz matricesare given by constructing the special transformation matrices. And an example is provided to verify the feasibility of the formulas.

generalized Loeplitz matrix, determinant, inverse, Lucas number.

Article Details

How to Cite
Chen, X. (2019). Exact Determinants and Inverses of Skew Symmetric Generalized Loeplitz Matrices. Journal of Advances in Mathematics and Computer Science, 33(6), 1-11. https://doi.org/10.9734/jamcs/2019/v33i630196
Original Research Article


Mukhexjee BN, Maiti SS. On some properties of positive definite Toeplitz matrices and their possible applications. Linear Algebra Appl. 1988;102:211-240.

Wen YW, Ng MK, Ching WK. A note on inversion of Toeplitz matrices. Appl. Math. Lett. 2004;17:903-907.

Akbulak M, Bozkurt D. On the norms of Toeplitz matrices involving Fibonacci and Lucas numbers. Hacet. J. Math. Stat. 2008;37:89-95.

Labahn G. Inversion of Toeplitz structured matrices using only standard equations. Linear Algebra Appl. 1994;207:49-70.

Jiang ZL, Gong YP, Gao Y. Invertibility and explicit inverses of circulant-type matrices with k-Fibonacci and k-Lucas numbers. Abstr. Appl. Anal. 2014;2014:1-10.

Jiang ZL, Gong YP, Gao Y. Circulant type matrices with the sum and product of Fibonacci and Lucas numbers. Abstr. Appl. Anal. 2014;2014(3):1-12.

Heining G, Rost K. Algebraic methods for toeplitz-like matrices and operators. Akademie- Verlag. Berlin; 1984.

Zhou JW, Jiang ZL. The spectral norms of g-circulant matrices with classical Fibonacci and Lucas numbers entries. Appl. Math. Comput. 2014;233:582-587.

Chen XT, Jiang ZL, Wang JM. Determinants and inverses of fibonacci and lucas skew symmetric toeplitz matrices. British J. Math. Comput. Sci. 2016;19(2):1-21.

Chen XT. Determinants and inverses of skew symmetric generalized foeplitz matrices. J. Adv. Math. Comput. Sci. 2019;33(4):1-12.

Liu L, Jiang ZL. Explicit form of the inverse matrices of Tribonacci circulant type matrices. Abstr. Appl. Anal. 2015;2015:10. Article ID 169726.