The splitting number can be smaller than the matrix chaos number

Let χ be the minimum cardinality of a subset of ^ω2 that cannot be made convergent by multiplication with a single Toeplitz matrix. By an application of a creature forcing we show that S-fraktur sign < χ is consistent. We thus answer a question by Vojtáš. We give two kinds of models for the strict inequality. The first is the combination of an א₂-iteration of some proper forcing with adding א₁ random reals. The second kind of models is obtained by adding δ random reals to a model of MA_<κ for some δ ∈ [א₁, κ). It was a conjecture of Blass that S-fraktur sign = א ₁ < χ = κ holds in such a model. For the analysis of the second model we again use the creature forcing from the first model.