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Linear operators preserving correlation matrices

Author(s): Chi-Kwong Li; Steve Pierce
Journal: Proc. Amer. Math. Soc. 131 (2003), 55-63.
MSC (2000): Primary 15A04
Posted: May 8, 2002
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Abstract | References | Similar articles | Additional information

Abstract: The linear operators that map the set of real or complex (rank one) correlation matrices onto itself are characterized.

References:

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
4.: E. Deutsch and H. Schneider, Bounded groups and norm-hermitian matrices, Linear Algebra Appl. 9 (1974), 9-27. MR 52:3200
5.: 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: 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
Copyright of article: Copyright 2002, American Mathematical Society


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