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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
Published electronically: May 8, 2002
MathSciNet review: 1929023
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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 [Enhancements On Off] (What's this?)

  • 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. Claude Chevalley, Theory of Lie Groups. I, Princeton Mathematical Series, vol. 8, Princeton University Press, Princeton, N. J., 1946. MR 0015396
  • 4. Emeric Deutsch and Hans Schneider, Bounded groups and norm-Hermitian matrices, Linear Algebra and Appl. 9 (1974), 9–27. MR 0382315
  • 5. A survey of linear preserver problems, Gordon and Breach Science Publishers, Yverdon, 1992. Linear and Multilinear Algebra 33 (1992), no. 1-2. MR 1346777

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Additional Information

Chi-Kwong Li
Affiliation: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187

Steve Pierce
Affiliation: Department of Mathematical Sciences, San Diego State University, San Diego, California 92182

Keywords: Correlation matrix, linear operator
Received by editor(s): October 17, 2000
Received by editor(s) in revised form: August 18, 2001
Published electronically: May 8, 2002
Additional Notes: Research supported by an NSF grant
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society