Let $A$ be a symmetric diagonal matrix in which $(A)_{ii} \geq 0$. Should one conclude that this matrix is positive semidefinite?
[Math] Is a symmetric diagonal matrix in which every entry is non-negative positive semidefinite
linear algebra
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- $x^TAx=\sum_{i=1}^{n}A_{ii}x_i^2\geq0, \forall x \in \mathbb{R^n}-{\theta_n}$.