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Large N matrix quantum mechanics is central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a "bootstrap" methodology. In this approach, operator expectation values are related by symmetries-such as time translation and SU(N) gauge invariance-and then bounded with certain positivity constraints. We first demonstrate how this method efficiently solves the conventionaldoi:10.1103/physrevlett.125.041601 pmid:32794829 fatcat:xljc6swelbccljibppusxspnke