Show example that the sum of two positive semi-definite matrices can be positive definite.
2026-03-29 04:41:33.1774759293
sum of two positive semi-definite matrices can be positive definite
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$\begin{pmatrix}1&0\\0&0\end{pmatrix}$ and $\begin{pmatrix}0&0\\0&1\end{pmatrix}.$