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Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces

Author

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  • Arnon Ploymukda
  • Pattrawut Chansangiam

Abstract

We introduce the notion of Khatri-Rao product for operator matrices acting on the direct sum of Hilbert spaces. This notion generalizes the tensor product and Hadamard product of operators and the Khatri-Rao product of matrices. We investigate algebraic properties, positivity, and monotonicity of the Khatri-Rao product. Moreover, there is a unital positive linear map taking Tracy-Singh products to Khatri-Rao products via an isometry.

Suggested Citation

  • Arnon Ploymukda & Pattrawut Chansangiam, 2016. "Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces," Journal of Mathematics, Hindawi, vol. 2016, pages 1-7, November.
    • Handle: RePEc:hin:jjmath:8301709
    DOI: 10.1155/2016/8301709
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    References listed on IDEAS

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    1. Huamin Zhang & Feng Ding, 2013. "On the Kronecker Products and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, June.
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