Demmel¶
An \(n \times n\) Demmel matrix is of the form
\[D(n,\beta) = (\beta J(-\beta^{-1},n))^{-1},\]
where \(J(-\beta^{-1},n)\) is the \(n \times n\) Jordan block with eigenvalue \(-\beta^{-1}\), and the standard value for \(\beta\) is \(10^{4/(n-1)}\). More explicitly, \(D(n,\beta)\) is an upper-triangular matrix where the \(j\)’th super-diagonal is equal to \(-\beta^j\).