# Quaternionic determinants

## Related Articles

- minor. // Hutchinson Dictionary of Scientific Biography;2005, p1
minor the mathematical theory of determinants, smaller determinant obtained by deleting one of the rows and one of the columns of a matrix.

- A fast algorithm for computing the determinants of the heptadiagonal matrices. Li Xin; Yang Liu // Advanced Materials Research;7/24/2014, Vol. 989-994, p1798
The cost of all existing algorithm for evaluating n th order determinants is at most O(nÂ³). This paper presents a new efficient computational algorithm for solving the determinants of the heptadiagonal matrices with cost O(n) only. It is a generalization of the DETGTRI algorithm. The...

- On the asymptotics of some large Hankel determinants generated by Fisherâ€“Hartwig symbols defined on the real line. Garoni, T. M. // Journal of Mathematical Physics;Apr2005, Vol. 46 Issue 4, p043516
We investigate the asymptotics of Hankel determinants of the form dctj,k=0N-1[âˆ«Î©dxÏ‰N(X)Â¦Â¦i=1mÂ¦Î¼i-XÂ¦2qiXj+k] as N â†’ âˆž with q and Î¼ fixed, where Î© is an infinite suhinterval of R and Ï‰N(x) is a positive weight on Î©. Such objects are natural...

- Toda lattice with a special self-consistent source. Urazboev, G. // Theoretical & Mathematical Physics;Feb2008, Vol. 154 Issue 2, p260
We describe a method for integrating the Toda lattice with a self-consistent source using the inverse scattering method for a discrete Sturm-Liouville operator with moving eigenvalues.

- Getting Smaller Dixon Dialytic Matrix Through Polynomials System Manipulating. Karimi, Seyed Mehdi; Reahman, Ali Bin Abd; Nor'aini bt Aris // Journal of Applied Sciences Research;Nov2011, Vol. 7 Issue 11, p1480
Resultant is the result of eliminating the variables from a system of polynomials. Compared with other matrix based methods such as Sylvester, Macaulay and Sturmfels et al, Dixon formulation is one of the most efficient tools to compute resultants. Previously it was thought that the Dixon...

- Some formulas for invariant phases of unitary matrices by Jarlskog. Suzuki, Tatsuo // Journal of Mathematical Physics;Dec2009, Vol. 50 Issue 12, p123526
We describe a calculation of Jarlskogâ€™s determinant in the case of n=4 in detail. Next, we investigate some formulas for invariant phases of unitary matrices and derive some explicit relations for them.

- Estimate on the second Hankel determinant for a subclass of quasi-convex functions. Goh, Jiun Shyan; Janteng, Aini // AIP Conference Proceedings;Sep2013, Vol. 1557 Issue 1, p401
In this paper, we consider the class KÎ±* of the functions of the form f(z) = z+a2z2+... which are analytic univalent in the disc D = {z:|z|<1} such that Re

Î±(z2f"(z))â€²/gâ€²(z)+(zfâ€²(z))â€²/g;(z) >0 where g âˆˆ C. This paper focuses on the functional... - Explicit Form of the Inverse Matrices of Tribonacci Circulant Type Matrices. Liu, Li; Jiang, Zhaolin // Abstract & Applied Analysis;3/19/2015, Vol. 2015, p1
It is a hot topic that circulant type matrices are applied to networks engineering. The determinants and inverses of Tribonacci circulant type matrices are discussed in the paper. Firstly, Tribonacci circulant type matrices are defined. In addition, we show the invertibility of Tribonacci...

- Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix. Zheng, Yanpeng; Shon, Sugoog // Abstract & Applied Analysis;3/19/2015, Vol. 2015, p1
The well known circulant matrices are applied to solve networked systems. In this paper, circulant and left circulant matrices with the Fermat and Mersenne numbers are considered. The nonsingularity of these special matrices is discussed. Meanwhile, the exact determinants and inverse matrices of...

- VanderLaan Circulant Type Matrices. Pan, Hongyan; Jiang, Zhaolin // Abstract & Applied Analysis;1/15/2015, Vol. 2015, p1
Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, and g-circulant matrices. The nonsingularity of these special matrices is...