Proposition 41.11.5.label Let $S$ be a matrix ordered space, then the mapping
\[\text{hom}(S; M_{n}(\complex)) \to \text{hom}(M_{n}(S); \complex) \quad \angles{E_{ij} \otimes a, \phi}_{M_n(S)}= \phi(a)_{ij}\]
induces an isomorphism $\text{hom}(M_{n}(S); \complex) \iso \text{hom}(S; M_{n}(\complex))$.
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