Suppose we have $\mathbf{v} \in \mathbb{C}^n$ as a row vector and $\mathbf{A} \in \mathbb{C}^{n \times n}$ and $\mathbf{A}$ is PSD matrix. Let: $w \triangleq \mathbf{v}\mathbf{A}\mathbf{v}^{H}$. Can we write the following inequality based on $w$,
$$\text{Tr}(\mathbf{A}) \leq K, $$
where $K \in \mathbb{R}_{+}$.