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A characterization theorem for matrix variances

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Abstract

Some recent papers formulated sufficient conditions for the decomposition of matrix variances [6, 10]. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of observables and we present a necessary and sufficient condition for the decomposition of the matrix variances.

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Acknowledgement

This work was partially supported by the Hungarian Research Grant OTKA K104206 and we are grateful to Prof. G. Tóth for communication. The authors wish to thank the referees for their constructive comments and advices.

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Authors and Affiliations

  1. Department of Mathematical Analysis, Budapest University of Technology and Economics, Egry József u. 1, Budapest, 1111, Hungary

    Dénes Petz & Dániel Virosztek

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  1. Dénes Petz
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  2. Dániel Virosztek
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Correspondence to Dénes Petz.

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Communicated by L. Kérchy

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Petz, D., Virosztek, D. A characterization theorem for matrix variances. ActaSci.Math. 80, 681–687 (2014). https://doi.org/10.14232/actasm-013-789-z

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  • DOI: https://doi.org/10.14232/actasm-013-789-z

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