Khatri-Rao sums for Hilbert space operators
We generalize the notions of Khatri-Rao sums for matrices and tensor sums for Hilbert space operators to KhatriRao sums for Hilbert space operators. This kind of operator sum is compatible with algebraic operations and order relations. We investigate its analytic properties, including continuity,...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Prince of Songkla University
2018-06-01
|
| Series: | Songklanakarin Journal of Science and Technology (SJST) |
| Subjects: | |
| Online Access: | https://rdo.psu.ac.th/sjstweb/journal/40-3/14.pdf |
| Summary: | We generalize the notions of Khatri-Rao sums for matrices and tensor sums for Hilbert space operators to KhatriRao
sums for Hilbert space operators. This kind of operator sum is compatible with algebraic operations and order relations.
We investigate its analytic properties, including continuity, convergence, and norm bounds. We also discuss the role of
selection operator that relates Khatri-Rao sums to Tracy-Singh sums and Khatri-Rao products. Binomial theorem involving
Khatri-Rao sums and its consequences are then established.
|
|---|---|
| ISSN: | 0125-3395 |