Determinant and inverse of a Gaussian Fibonacci skew-Hermitian Toeplitz matrix
-
2287
Downloads
-
3677
Views
Authors
Zhaolin Jiang
- Department of Mathematics, Linyi University, Linyi 276000, P. R. China.
Jixiu Sun
- Department of Mathematics, Linyi University, Linyi 276000, P. R. China.
- School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China.
Abstract
In this paper, we consider the determinant and the inverse of the Gaussian Fibonacci skew-Hermitian Toeplitz matrix.
We first give the definition of the Gaussian Fibonacci skew-Hermitian Toeplitz matrix. Then we compute the determinant and
inverse of the Gaussian Fibonacci skew-Hermitian Toeplitz matrix by constructing the transformation matrices.
Share and Cite
ISRP Style
Zhaolin Jiang, Jixiu Sun, Determinant and inverse of a Gaussian Fibonacci skew-Hermitian Toeplitz matrix, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3694--3707
AMA Style
Jiang Zhaolin, Sun Jixiu, Determinant and inverse of a Gaussian Fibonacci skew-Hermitian Toeplitz matrix. J. Nonlinear Sci. Appl. (2017); 10(7):3694--3707
Chicago/Turabian Style
Jiang, Zhaolin, Sun, Jixiu. "Determinant and inverse of a Gaussian Fibonacci skew-Hermitian Toeplitz matrix." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3694--3707
Keywords
- Gaussian Fibonacci number
- skew-Hermitian Toeplitz matrix
- determinant
- inverse.
MSC
References
-
[1]
M. Akbulak, D. Bozkurt, On the norms of Toeplitz matrices involving Fibonacci and Lucas numbers, Hacet. J. Math. Stat., 37 (2008), 89–95.
-
[2]
D. Bozkurt, T.-Y. Tam, Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal-Lucas Numbers, Appl. Math. Comput., 219 (2012), 544–551.
-
[3]
A. Buckley, On the solution of certain skew symmetric linear systems, SIAM J. Numer. Anal., 14 (1977), 566–570.
-
[4]
R. H. Chan, X.-Q. Jin, Circulant and skew-circulant preconditioners for skew-Hermitian type Toeplitz systems, BIT, 31 (1991), 632–646.
-
[5]
X.-T. Chen, Z.-L. Jiang, J.-M. Wang, Determinants and inverses of Fibonacci and Lucas skew symmetric Toeplitz matrices, British J. Math. Comput. Sci., 19 (2016), 1–21.
-
[6]
L. Dazheng, Fibonacci-Lucas quasi-cyclic matrices, A special tribute to Calvin T. Long, Fibonacci Quart., 40 (2002), 280–286.
-
[7]
U. Grenander, G. Szegö, Toeplitz forms and their applications, California Monographs in Mathematical Sciences University of California Press, Berkeley-Los Angeles (1958)
-
[8]
G. Heining, K. Rost, Algebraic methods for Toeplitz-like matrices and operators, Mathematical Research, Akademie- Verlag, Berlin (1984)
-
[9]
A. F. Horadam, Further appearence of the Fibonacci sequence, Fibonacci Quart., 1 (1963), 41–42.
-
[10]
A. Ipek, K. Arı, On Hessenberg and pentadiagonal determinants related with Fibonacci and Fibonacci-like numbers, Appl. Math. Comput., 229 (2014), 433–439.
-
[11]
Z.-L. Jiang, Y.-P. Gong, Y. Gao, Circulant type matrices with the sum and product of Fibonacci and Lucas numbers, Abstr. Appl. Anal., 2014 (2014), 12 pages.
-
[12]
Z.-L. Jiang, Y.-P. Gong, Y. Gao, Invertibility and explicit inverses of circulant-type matrices with k-Fibonacci and k-Lucas numbers, Abstr Appl. Anal., 2014 (2014), 10 pages.
-
[13]
X.-Y. Jiang, K.-C. Hong, Exact determinants of some special circulant matrices involving four kinds of famous numbers, Abstr. Appl. Anal., 2014 (2014), 12 pages.
-
[14]
X.-Y. Jiang, K.-C. Hong, Explicit inverse matrices of Tribonacci skew circulant type matrices, Appl. Math. Comput., 268 (2015), 93–102.
-
[15]
X.-Y. Jiang, K.-C. Hong, Skew cyclic displacements and inversions of two innovative patterned matrices, Appl. Math. Comput., 308 (2017), 174–184.
-
[16]
Z.-L. Jiang, J.-W. Zhou, A note on spectral norms of even-order r-circulant matrices, Appl. Math. Comput., 250 (2014), 368–371.
-
[17]
J. Li, Z.-L. Jiang, F.-L. Lu, Determinants, norms, and the spread of circulant matrices with Tribonacci and generalized Lucas numbers, Abstr. Appl. Anal., 2014 (2014), 9 pages.
-
[18]
L. Liu, Z.-L. Jiang, Explicit form of the inverse matrices of Tribonacci circulant type matrices, Abstr. Appl. Anal., 2015 (2015), 10 pages.
-
[19]
M. Merca, A note on the determinant of a Toeplitz-Hessenberg matrix, Spec. Matrices, 2 (2014), 10–16.
-
[20]
B. N. Mukherjee, S. S. Maiti, On some properties of positive definite Toeplitz matrices and their possible applications, Linear Algebra Appl., 102 (1988), 211–240.
-
[21]
L. Rodman, Pairs of Hermitian and skew-Hermitian quaternionic matrices: canonical forms and their applications, Linear Algebra Appl., 429 (2008), 981–1019.
-
[22]
S.-Q. Shen, J.-M. Cen, Y. Hao, On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers, Appl. Math. Comput., 217 (2011), 9790–9797.
-
[23]
J.-X. Sun, Z.-L. Jiang, Computing the determinant and inverse of the complex Fibonacci Hermitian Toeplitz matrix, British J. Mathe. Comput. Sci., 19 (2016), 1–16.
-
[24]
Y.-P. Zheng, S.-G. Shon, Exact determinants and inverses of generalized Lucas skew circulant type matrices, Appl. Math. Comput., 270 (2015), 105–113.
-
[25]
Y.-P. Zheng, S.-G. Shon, J.-Y. Kim, Cyclic displacements and decompositions of inverse matrices for CUPL Toeplitz matrices, J. Math. Anal. Appl., 455 (2017), 727–741.
-
[26]
J.-W. Zhou, Z.-L. Jiang, The spectral norms of g-circulant matrices with classical Fibonacci and Lucas numbers entries, Appl. Math. Comput., 233 (2014), 582–587.