Schur-Like Forms for Matrix Lie Groups , Lie Algebras and Jordan Algebras

@inproceedings{Ammar1999SchurLikeFF,
  title={Schur-Like Forms for Matrix Lie Groups , Lie Algebras and Jordan Algebras},
  author={Gregory S. Ammar},
  year={1999}
}
We describe canonical forms for elements of a classical Lie group of matrices under similarity transformations in the group. Matrices in the associated Lie algebra and Jordan algebra of matrices inherit related forms under these similarity transformations. In general, one cannot achieve diagonal or Schur form, but the form that can be achieved displays the eigenvalues of the matrix. We also discuss matrices in intersections of these classes and their Schur-like forms. Such multistructured… CONTINUE READING
Highly Cited
This paper has 95 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 28 references

Numerical simulation in particle physics

F. Karsch, E. Laermann
Rep. Prog. Phys., 56:1347{1395 • 1993
View 1 Excerpt

A chart of numerical methods for structured eigenvalue problems

A. Bunse-Gerstner, R. Byers, V. Mehrmann
SIAM J. Matrix Anal. Appl., 13:419{453 • 1992
View 3 Excerpts

A kqz algorithm for solving linear- response eigenvalue equations

U. Flaschka, W.-W. Lin, J.-L. Wu
Linear Algebra Appl., 165:93{123 • 1992
View 3 Excerpts

Eine Variante des Lanczos-Algorithmus f ur gro e

U. Flaschka
d unn be- setzte symmetrische Matrizen mit Blockstruktur. Dissertation, Universit at Bielefeld, Bielefeld, Germany • 1992
View 3 Excerpts

The Autonomous Linear Quadratic Control Problem, The- ory and Numerical Solution. Number 163 in Lecture Notes in Control and Information Sciences

V. Mehrmann
1991
View 3 Excerpts

On Schur type decompositions for Hamiltonian and symplectic pencils

W.-W. Lin, T.-C. Ho
Technical report, Institute of Applied Mathematics, National Tsing Hua University, Taiwan • 1990
View 1 Excerpt

Numerical solution for algebraic Riccati equations

A. Bunse-Gerstner, R. Byers, V. Mehrmann
S. Bittanti, editor, Proceedings of the Work- shop on The Riccati Equation in Control, Systems and Signals, pages 107{ 115, Bologna, Italy • 1989
View 1 Excerpt

and P

J. Olson, H. Jensen
J rgensen. Solution of large matrix equations which occur in response theory. J. Comput. Phys., 74:265{282 • 1988
View 2 Excerpts

Determination of Pisarenko frequency estimates as eigenvalues of an orthogonal matrix

G. S. Ammar, W. B. Gragg, L. Reichel
F. T. Luk, editor, Advanced Algorithms and Architectures for Signal Processing II, pages 143{145. SPIE • 1987
View 1 Excerpt