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Dec 30, 2012 at 11:48 vote accept Uday
Dec 27, 2012 at 16:35 comment added Uday @Suvrit Thank you for the answer. Your answer settles the fact that there exists a solution. But, my original interest, which I unfortunately did not make it clear in my post, is to get some quantitative information on the bounds of the solution w.r.t the eigenvalues of $A$ and $B$.
Dec 27, 2012 at 11:25 history answered Suvrit CC BY-SA 3.0