SupplementaryMaterial: ProbabilisticLinear SolversforMachineLearning

This supplement complements the paperProbabilistic Linear Solvers for Machine Learningand is structured as follows. SectionS2introducesdifferent variants of Kronecker products used to define matrix-variate normal distributions in Section S3. Finally, Section S7 provides some background for the application of probabilistic linear solvers to the solution of discretized partial differentialequations. At first glance it might seem counterintuitive to frame a numerical problem in the language of probability theory. After all,when considering theexactproblemAx =ballquantities involved A,x, and b are deterministic. Characteristic properties of Kronecker-type products are useful to turn matrix equations intovectorequations.