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The little Grothendieck problem consists of maximizing $\sum_{ij}C_{ij}x_ix_j$ over binary variables $x_i\in\{\pm1\}$, where C is a positive semidefinite matrix.
Some metric inequalities in the space of matrices
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Three-dimensional structure determination from common lines in Cryo-EM by eigenvectors and semidefinite programming
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Random matrices and communication systems: Wishart random matrices: marginal eigenvalue distribution
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Tight hardness of the non-commutative Grothendieck problem
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Global registration of multiple point clouds using semidefinite programming
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