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Likewise, given a tuple $B=(B_1,\\dots,B_g)$ of $e\\times e$ matrices the collection of tuples of matrices $X=(X_1,\\dots,X_g)$ (of the same size) such that $I + \\sum B_j\\otimes X_j +\\sum B_j^* \\otimes X_j^*\\succeq 0$ is a free spectrahedron $\\mathcal D_B$. 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