A _superoperator_ is a [Linear map](Linear%20map.md) that maps a [Linear operator](Linear%20operator.md) to another linear operator. Thus it is a also a linear map between [spaces of linear operators.](Spaces%20of%20linear%20operators) %%This topic is highly motivated by quantum information - see preskill's notes page 93 for the most basic definition that I use here.%% %%Does this concept only exist in quantum information or is there some more general notion?%% _The definition as stated here is a concept exclusively used in quantum information science since it applies exclusively to quantum density operators, however this mathematical formulation may find applications or close analogs in other fields._ #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/VectorSpaces #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/Operators #QuantumMechanics/MathematicalFoundations