I am doing some research that relies on Hadamard product of two matrices bound, the most famous one that I encounter is : $\rho(A\circ B)=\rho(A)\rho(B)$ this seems to be trivial when I test it with random matrices, however I have difficulty finding a good proof for it. I've found this bound from the following paper: http://www.journalofinequalitiesandapplications.com/content/pdf/1029-242X-2013-433.pdf where they are trying to improve it.
2025-01-13 00:13:29.1736727209
Spectrum radius upper bound of Hadamard product
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