For , let be a random matrix, a real deterministic matrix, and the corresponding structured random matrix. We study the expected operator norm of considered as a random operator between and for . We prove optimal bounds up to logarithmic terms when the underlying random matrix has i.i.d. Gaussian entries, independent mean-zero bounded entries, or independent mean-zero ( ) entries. In certain cases, we determine the precise order of the expected norm up to constants. Our results are expressed through a sum of operator norms of Hadamard products and .
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| http://dx.doi.org/10.1007/s00208-023-02599-6 | DOI Listing |
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