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PositiveDefiniteMatrixQ[{{1/2+0.001, 1/2, 1/2}, {1/2, 1/2+0.001, 1/2}, {1/2, 1/2, 1/2+0.001}}]
PositiveDefiniteMatrixQ[{{1/2+0.001, 1/2, 1/2}, {1/2, 1/2+0.001, 1/2}, {1/2, 1/2, 1/2+0.001}}]
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