[Math] Is a symmetric diagonal matrix in which every entry is non-negative positive semidefinite

linear algebra

Let $A$ be a symmetric diagonal matrix in which $(A)_{ii} \geq 0$. Should one conclude that this matrix is positive semidefinite?

Best Answer

Yes, because- $x^TAx=\sum_{i=1}^{n}A_{ii}x_i^2\geq0, \forall x \in \mathbb{R^n}-{\theta_n}$.

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