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This paper shows that $t_m \leq \|\mathbf{A}\|_\infty \leq \sqrt{t_m}$ holds,when $\mathbf{A} \in \mathbb{R}^{m \times m}$ is a Runge-Kutta matrix whichnodes originating from the Gaussian quadrature that integrates polynomials ofdegree $2m-2$ exactly. It can be shown that this is also true for theGauss-Lobatto quadrature. Additionally, the characteristic polynomial of$\mathbf{A}$, when the matrix is nonsingular, is $p_A(\lambda) = m!t^m +(m-1)!a_{m-1}t^{m-1} + \dots + a_0$, where the coefficients $a_i$ are thecoefficients of the polynomial of nodes $\omega(t) = (t - t_1) \dots (t - t_m)= t^m + a_{m-1}t^{m-1} + \dots + a_0$.

The infinity norm bounds and characteristic polynomial for high order RK matrices