Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / P / 4 / d / Solution

The Gershgorin discs of $A^{\mathsf{T}}$ have radii $1/4,q,\dots ,q,ϵ$. They too are disjoint and have one eigenvalue each. The disc centered at $n$ therefore improves the final bound toIt selects the same eigenvalue as before because all other discs lie a fixed positive distance from the disc centered at $n$.