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- W2016075531 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." @default.
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- W2016075531 date "1979-09-01" @default.
- W2016075531 modified "2023-09-26" @default.
- W2016075531 title "Separation theorems for singular values of matrices and their applications in multivariate analysis" @default.
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- W2016075531 doi "https://doi.org/10.1016/0047-259x(79)90094-0" @default.
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