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

الملخص EN

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.