151
Views
5
CrossRef citations to date
0
Altmetric
Articles

A topological approach to left eigenvalues of quaternionic matrices

&
Pages 139-158 | Received 10 Oct 2012, Accepted 16 Nov 2012, Published online: 24 Jan 2013

References

  • Wood RMW. Quaternionic eigenvalues. Bull. Lond. Math. Soc. 1985;17:137–138.
  • Zhang F. Quaternions and matrices of quaternions. Linear Algebra Appl. 1997;251:21–57.
  • Zhang F. Geršgorin type theorems for quaternionic matrices. Linear Algebra Appl. 2007;424:139–153.
  • Huang L, So W. On left eigenvalues of a quaternionic matrix. Linear Algebra Appl. 2001;323:105–116.
  • Macías-Virgós E, Pereira-Sáez MJ. Left eigenvalues of 2×2 symplectic matrices. Electron. J. Linear Algebra. 2009;18:274–280.
  • Gelfand I, Gelfand S, Retakh V. Lee Wilson R. Quasideterminants. Adv. Math. 2005;193:56–141.
  • Dieudonné J. A history of algebraic and differential topology 1900–1960. Boston: Modern Birkhäuser Classics; 2009.
  • Ambrosetti A, Malchiodi A. Nonlinear analysis and semilinear elliptic problems. Cambridge studies in advanced mathematics. Cambridge: Cambridge University Press; 2007.
  • Deimling K. Nonlinear functional analysis. Berlin: Springer-Verlag; 1985.
  • Pumplün S, Walcher S. On the zeros of polynomials over quaternions. Commun. Algebra. 2002;30:4007–4018.
  • Madsen I, Tornehave J. From calculus to cohomology: de Rham cohomology and characteristic classes. Cambridge: Cambridge University Press; 1997.
  • Massey WS. A basic course in algebraic topology. Graduate Texts in Mathematics. Vol. 127. New York (NY): Springer-Verlag; 1991.
  • Johnson RE. On the equationχα=χγ+β over an algebraic division ring. Bull. Am. Math. Soc. 1944;50:202–207.
  • Janovská D, Opfer G. Linear equations in quaternionic variables. Mitt. Math. Ges. Hamb. 2008;27:223–234.
  • Georgiev G, Ivanov I, Mihaylova M, Dinkova T. An algorithm for solving a Sylvester quaternion equation. Proc. Annual Conf. Rousse Univ. Sc. Union. 2009;48:35–39.
  • Aslaksen H. Quaternionic determinants. Math. Intell. 1996;18:57–65.
  • Cohen N, Leo S. The quaternionic determinant. Electron. J. Linear Algebra. 2000;7:100–111.
  • Nanson J. On certain determinant theorems. J. Reine Angew. Math. 1900;122:179–185.
  • Farenick DR, Pidkowich BAF. The spectral theorem in quaternions. Linear Algebra Appl. 2003;371:75–102.
  • Kyrchei II. Determinantal representations of the Moore-Penrose inverse over the quaternion skew field and corresponding Cramer’s rules. Linear Multilinear A. 2011;59:413–431.
  • Gelfand IM, Retakh VS. A theory of noncommutative determinants and chracterisitic functions of graphs. Funct. Anal. Appl. 1992;26:1–20.
  • So W. Quaternionic left eigenvalue problem. Southeast Asian Bull. Math. 2005;29:555–565.
  • Huang L. On two questions about quaternion matrices. Linear Algebra Appl. 2000;318:79–86.
  • Eilenberg S, Steenrod N. Foundations of algebraic topology. Princeton mathematical series, No.15. Princeton: University Press, XIV; 1952.
  • Farid FO, Wang Q-W, Zhang F. On the eigenvalues of quaternion matrices. Linear Multilinear A. 2011;59:451–473.
  • Huang L, So W. Quadratic formulas for quaternions. Appl. Math. Lett. 2002;15:533–540.
  • Janovská D, Opfer G. The classification and the computation of the zeros of quaternionic, two-sided polynomials. Numer. Math. 2010;115:81–100.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.