How to write this QP in CVX form

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A, B, X are all matrices, A is semidefinite so I think this question is convex, how can I write it into a form that can be accepted by CVX?

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With the conditions stated, this is not necessarily convex, even in the scalar case. For instance, A = 1, B = -1.

In the matrix case, it’s not obvious to me that B (and A) being psd would be sufficient to guarantee convexity; so you’d have to prove it was sufficient.