Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces
Copyright policy )Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces
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.
Hadamard product, Deformations and Structures of Hom-Lie Algebras, positivity, Khatri-Rao product for operator matrices, Geometry, Tensor products of linear operators, Operator (biology), Matrix Inequalities and Geometric Means, Mathematical analysis, Gene, Biochemistry, direct sum of Hilbert spaces, Operators on Hilbert spaces (general), QA1-939, FOS: Mathematics, Operator matrices, Hadamard transform, Matrix Algorithms and Iterative Methods, Product (mathematics), Algebra over a field, Algebra and Number Theory, Isometry (Riemannian geometry), Applied Mathematics, Hilbert space, Pure mathematics, monotonicity, Tensor product, Chemistry, Computational Theory and Mathematics, Computer Science, Physical Sciences, Repressor, Transcription factor, Mathematics, Monotonic function, Matrix Computations
Hadamard product, Deformations and Structures of Hom-Lie Algebras, positivity, Khatri-Rao product for operator matrices, Geometry, Tensor products of linear operators, Operator (biology), Matrix Inequalities and Geometric Means, Mathematical analysis, Gene, Biochemistry, direct sum of Hilbert spaces, Operators on Hilbert spaces (general), QA1-939, FOS: Mathematics, Operator matrices, Hadamard transform, Matrix Algorithms and Iterative Methods, Product (mathematics), Algebra over a field, Algebra and Number Theory, Isometry (Riemannian geometry), Applied Mathematics, Hilbert space, Pure mathematics, monotonicity, Tensor product, Chemistry, Computational Theory and Mathematics, Computer Science, Physical Sciences, Repressor, Transcription factor, Mathematics, Monotonic function, Matrix Computations
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