Say M_{ij} = A_{ij} + s B_{ij}/2, where the matrices are 3 by3 and A_{ij} symmetric, s \in [0,s^*], and the smallest eigenvalue of A is lambda \leq -(1/2). Given that |M_{ij} - A_{ij}| \leq to C_{s^*} s/2 and |A_{ij}| \leq 1, plus that the cubic equation determining the eigenvalues has an explicit fomrula to solve, how do you show that there is some s_0 \in [0,s^*] such that M_{ij} has an eigenvalue \leq -(1/4)?(adsbygoogle = window.adsbygoogle || []).push({});

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# Estimating eigenvalue of perturbed matrix

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