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

Ploymukda, Arnon; Chansangiam, Pattrawut

doi:10.1155/2016/8301709

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

Author(s)

Ploymukda, Arnon

Chansangiam, Pattrawut

Date Issued

January 1, 2016

Type

Article

DOI

10.1155/2016/8301709

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.

Citation

Journal of Mathematics, 2016, 2016