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Some further matrix extensions of the Cauchy-Schwarz and Kantorovich inequalities, with some statistical applications. (English) Zbl 0860.15021

The paper considers what happens to the inequalities of Cauchy-Schwarz and Kantorovich when the vectors are replaced by matrices, the positive definite matrix is allowed to be positive semidefinite singular and the usual inequalities are replaced by Löwner partial orderings. Some examples in the context of linear statistical models are also presented.

MSC:

15A45 Miscellaneous inequalities involving matrices
62J05 Linear regression; mixed models
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