Commutators of skew-symmetric matrices

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 15, Issue 3, 2005, Pages 793-801

  Bloch, Anthony M ^a   Iserles, Arieh ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Commutator matrices; Lie algebras; Symmetric gauges

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; INTEGRATION; MATHEMATICAL OPERATORS; SET THEORY; THEOREM PROVING; VECTORS;

BANACH INEQUALITY; COMMUTATOR MATRICES; LIE ALGEBRA; SYMMETRIC GAGES;

MATRIX ALGEBRA;

EID: 21144453106     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127405012417     Document Type: Conference Paper

References (13)

1. Brockett, R. [1993] "Differential geometry and the design of gradient algorithms," Proc. Symp. Pure Math. 54, 69-92.
2. Brockett, R. [1994] "Differential equations and matrix inequalities on isospectral families," Lin. Alg. Appl. 203/204, 189-207.
3. Carter, R., Segal, G. & Macdonald, I. [1995] Lectures on Lie Groups and Lie Algebras (Cambridge University Press, Cambridge).
4. Chartrand, G. & Lesniak, L. [1986] Graphs and Digraphs (Wadsworth & Brooks/Cole).
5. Hille, E. [1969] Lectures on Ordinary Differential Equations (Addison-Wesley, Reading, MA).
6. Horn, R. A. & Johnson, C. R. [1994] Topics in Matrix Analysis (Cambridge University Press, Cambridge).
7. Humphreys, J. E. [1978] Introduction to Lie Algebras and Representation Theory (Springer-Verlag, Berlin).
8. Iserles, A., Munthe-Kaas, H. Z., Nørsett, S. P. & Zanna, A. [2000] "Lie-group methods," Acta Numerica 9, 215-365.
9. Kobayashi, S. & Nomizu, K. [1969] Foundations of Differential Geometry (John Wiley, NY).
10. Marsden, J. E. & Ratiu, T. [1984] Introduction to Mechanics and Symmetry (Springer-Verlag, NY).
11. Varadarajan, V. S. [1984] Lie Groups, Lie Algebras, and Their Representations (Springer-Verlag, NY).
12. von Neumann, J. [1937] "Some matrix inequalities and metrization of matrix space," Tomsk Univ. Rev. 1, 286-300;
13. Reprinted [1962] in Collected Works (Pergamon, Oxford), Vol. IV, pp. 205-218.