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Linear operators preserving correlation matrices
Authors:
Chi-Kwong Li and Steve Pierce
Journal:
Proc. Amer. Math. Soc. 131 (2003), 55-63
MSC (2000):
Primary 15A04
Posted:
May 8, 2002
MathSciNet review:
1929023
Full-text PDF Free Access
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Abstract: The linear operators that map the set of real or complex (rank one) correlation matrices onto itself are characterized.
- 1.
H. Auerbach, Sur les groupes bornés de substitutions, linéaires, C.R. Acad. Sci. Paris 195 (1932), 1367-1369.
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M.D. Choi, Positive linear maps, Proceedings of Symposia in Pure Math., Amer. Math. Soc. 38 (2) (1982), 583-590.
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Claude
Chevalley, Theory of Lie Groups. I, Princeton Mathematical
Series, vol. 8, Princeton University Press, Princeton, N. J., 1946. MR 0015396
(7,412c)
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Emeric
Deutsch and Hans
Schneider, Bounded groups and norm-Hermitian matrices, Linear
Algebra and Appl. 9 (1974), 9–27. MR 0382315
(52 #3200)
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1-2. MR
1346777 (96c:15043)
- 1.
- H. Auerbach, Sur les groupes bornés de substitutions, linéaires, C.R. Acad. Sci. Paris 195 (1932), 1367-1369.
- 2.
- M.D. Choi, Positive linear maps, Proceedings of Symposia in Pure Math., Amer. Math. Soc. 38 (2) (1982), 583-590.
- 3.
- C. Chevalley, Theory of Lie groups, Princeton University Press, Princeton, 1946. MR 7:412c
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- E. Deutsch and H. Schneider, Bounded groups and norm-hermitian matrices, Linear Algebra Appl. 9 (1974), 9-27. MR 52:3200
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- S. Pierce et. al., A Survey on Linear Preserver Problems, Linear and Multilinear Algebra 33 (1992), 1-129. MR 96c:15043
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Additional Information
Chi-Kwong Li
Affiliation:
Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187
Email:
ckli@math.wm.edu
Steve Pierce
Affiliation:
Department of Mathematical Sciences, San Diego State University, San Diego, California 92182
Email:
pierce@math.sdsu.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-02-06508-5
PII:
S 0002-9939(02)06508-5
Keywords:
Correlation matrix,
linear operator
Received by editor(s):
October 17, 2000
Received by editor(s) in revised form:
August 18, 2001
Posted:
May 8, 2002
Additional Notes:
Research supported by an NSF grant
Communicated by:
Joseph A. Ball
Article copyright:
© Copyright 2002 American Mathematical Society
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