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In literature, people say a spectrahedron is the following set

$$\left\{x \in \mathbb{R}^d : x_1 A_1 + \cdots + x_d A_d \geq B \right\}$$

where $\geq$ is in the positive semidefinite sense. Is there a name for the set where one further restricts matrices $\{A_i\}_i,B$ to also be positive semidefinite?

This seems natural to me, but do not see people having looked at it, but also I am not sure what to google to understand this better.

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  • $\begingroup$ Sure, I agree with that. I was more curious if they are just PSD but not diagonal, is there something known about such feasible sets (for example, do they have a name or are they interesting for other reasons?) $\endgroup$
    – wwjohnsmith
    Commented Jun 25, 2020 at 13:10

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