Let $K$ be a complete, non-trivially valued, ultrametric (or non-archimedean) field. We recall the notions of boundedness and convergence with speed and speed-Maddox spaces over $K$, where the speed is defined by a sequence $\mu=\{\mu_n\}$ in $K$ with the property $0<|\mu_n|\nearrow\infty$, $n\to\infty$, and define new notion of absolute convergence with speed $\mu$ over $K$. Let $\lambda$ be another speed in $K$. The necessary and sufficient conditions for a matrix $A$ over $K$ would transform all sequences that are $\lambda$-convergent or absolutely $\lambda$-convergent over $K$ into the speed-Maddox spaces over $K$, where the speed is defined by $\mu$.