# Name of real-valued representation of density matrix?

This is a specialization of my question https://math.stackexchange.com/q/3157300/ on math.SE.

There are many ways to write the density matrix $$\hat \rho$$ as vector $$\vec \rho$$. In the Liouville space, the matrix elements are simply stacked columnwise, i.e., $$\vec \rho = \mathrm{vec}(\hat \rho)$$, where the vector are mixed complex-/real-valued. The generalized Bloch vector or coherence vector representation removes the redundant information in the density matrix (trace equals 1, hermiticity) and features a real-valued vector.

An alternative representation that uses the hermiticity to remove most of the redundancy would be easy to construct. The resulting vector would contain the populations as well as real and imaginary part of one half of the off-diagonal elements/coherences. Is there a certain name for this arrangement or is it just too trivial and has no name? Additionally, is there a certain convention (similar to the conventions for the Pauli matrices that serve as basis for the Bloch vector construction)? Naming and/or convention suggestions also welcome.

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