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Separation theorems for singular values of matrices and their applications in multivariate analysis

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Author Info
Rao, C. Radhakrishna
Abstract

Separation theorems for singular values of a matrix, similar to the Poincaré separation theorem for the eigenvalues of a Hermitian matrix, are proved. The results are applied to problems in approximating a given r.v. by an r.v. in a specified class. In particular, problems of canonical correlations, reduced rank regression, fitting an orthogonal random variable (r.v.) to a given r.v., and estimation of residuals in the Gauss-Markoff model are discussed. In each case, a solution is obtained by minimizing a suitable norm. In some cases a common solution is shown to minimize a wide class of norms known as unitarily invariant norms introduced by von Neumann.

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Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 9 (1979)
Issue (Month): 3 (September)
Pages: 362-377
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Handle: RePEc:eee:jmvana:v:9:y:1979:i:3:p:362-377

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Related research
Keywords: Matrix approximations unitarily invariant norm canonical correlations multivariate linear regression estimation of residuals;

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Yoshio Takane & Tadashi Shibayama, 1991. "Principal component analysis with external information on both subjects and variables," Psychometrika, Springer, vol. 56(1), pages 97-120, March. [Downloadable!] (restricted)
  2. Cajo Braak, 1990. "Interpreting canonical correlation analysis through biplots of structure correlations and weights," Psychometrika, Springer, vol. 55(3), pages 519-531, September. [Downloadable!] (restricted)
  3. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," EERI Research Paper Series EERI_RP_2003_04, Economics and Econometrics Research Institute (EERI). [Downloadable!]
  4. J. Ramsay & Jos Berge & G. Styan, 1984. "Matrix correlation," Psychometrika, Springer, vol. 49(3), pages 403-423, September. [Downloadable!] (restricted)
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