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Eigenvalue completions by affine varieties
Author(s):
Joachim
Rosenthal;
Xiaochang
Wang
Journal:
Proc. Amer. Math. Soc.
128
(2000),
643-646.
MSC (2000):
Primary 15A18;
Secondary 93B60
Posted:
October 25, 1999
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Abstract:
In this paper we provide new necessary and sufficient conditions for a general class of eigenvalue completion problems.
References:
- [Bor91]
- A. Borel, Linear algebraic groups, second enlarged edition, Graduate Texts in Mathematics, vol. 126, Springer-Verlag, New York, 1991. MR 92d:20001
- [Byr89]
- C. I. Byrnes, Pole assignment by output feedback, Three Decades of Mathematical System Theory (H. Nijmeijer and J. M. Schumacher, eds.), Lect Notes in Control and Information Sciences # 135, Springer Verlag, 1989, pp. 31-78. MR 90k:93001
- [GKS95]
- I. Gohberg, M. A. Kaashoek, and F. van Schagen, Partially specified matrices and operators: Classification, completion, applications, Birkhäuser, Boston-Basel-Berlin, 1995. MR 97i:47002
- [HRW97]
- W. Helton, J. Rosenthal, and X. Wang, Matrix extensions and eigenvalue completions, the generic case, Trans. Amer. Math. Soc. 349 (1997 no. 8, 3401-3408.) MR 97m:15010
- [RW97]
- J. Rosenthal and X. Wang, Inverse eigenvalue problems for multivariabl linear systems, Systems and Control in the Twenty-First Century (Boston-Basel-Berlin) (C. I. Byrnes, B. N. Datta, D. Gilliam, and C. F. Martin, eds.), Birkäuser, Boston-Basel-Berlin, 1997, pp. 289-311. MR 97k:93027
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Additional Information:
Joachim
Rosenthal
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556-5683
Email:
Rosenthal.1@nd.edu
Xiaochang
Wang
Affiliation:
Department of Mathematics, Texas Tech University, Lubbock, Texas 79409-2013
Email:
mdxia@ttacs1.ttu.edu
DOI:
10.1090/S0002-9939-99-05655-5
PII:
S 0002-9939(99)05655-5
Keywords:
Eigenvalue completions,
pole placement problems,
dominant morphism theorem,
inverse eigenvalue problems
Received by editor(s):
March 4, 1997
Received by editor(s) in revised form:
April 2, 1998
Posted:
October 25, 1999
Additional Notes:
The first author was supported in part by NSF grant DMS-9400965.
The second author was supported in part by NSF grant DMS-9500594.
Communicated by:
John A. Burns
Copyright of article:
Copyright
1999,
American Mathematical Society
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