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The Cauchy-Schwarz inequality states $|\langle x,y \rangle |\leq ||x||\cdot ||y||.$ Use this tag for questions related to the CS inequality and its applications.
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An Linear Algebra Inequality
If you replace determinants by traces, then this inequality is just Cauchy-Schwarz for the inner product $(X,Y)=\mathop{\mathrm{tr}}(XY^T)$ on the space of matrices. Now, we just have to recall that d …