Liouville space
In the mathematical physics of quantum mechanics, Liouville space, also known as line space, is the space of operators on Hilbert space. Liouville space is itself a Hilbert space under the Hilbert-Schmidt inner product.
Abstractly, Liouville space is equivalent to the tensor product of a Hilbert space with its dual. A common computational technique to organize computations in Liouville space is vectorization.
Liouville space underlies the density operator formalism and is a common computation technique in the study of open quantum systems.