I have a matrix, $X = xx^T$, where $x \in \mathbb{R}^n$. Is the matrix $X$ semidefinite?
2026-02-23 05:09:50.1771823390
Is this rank-$1$ matrix semidefinite?
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For any vector $y$ one has $y^T X y=y^Txx^Ty = (y^Tx)^2$ (since $y^Tx=x^Ty$ is a scalar), so the answer is yes.