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On a Conjecture Related to Eigenvalue Perturbations
In connection with eigenvalue perturbation bounds, Li [Linear Algebra Appl., 278 (1998), pp. 317-326] formulated three minimization problems involving Hadamard products. The third asks how to relate $$ \min_{W\ \mathrm{nonsingular}}\|W\circ G\|_\mathrm{ui}\,\|W^{-1}\circ G^\mathrm{T}\|_\mathrm{ui} \
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