How well can an n\(\times n\) matrix be approximated by reducible ones? (Q1082600)

There exists a universal constant \(\alpha\), \(1.7\times 10^{-7}<\alpha <\), with the following property: for each \(n\geq 2\), there exists an \(n\times n\) complex matrix \(T_ n\), with \(\| T_ n\| =1\), such that \(\| T_ n-A\| \geq \alpha\) for every reducible matrix A. The article also includes several related results.