Consider the following block matrix: $$ A=\left(\begin{array}{ccccc} \sqrt{t} \mathbb{I}_{d_{1}} & \dot{\tilde{K}}_{0}^{\dagger} & \dot{\tilde{K}}_{1}^{\dagger} & \ldots & \dot{\tilde{K}}_{k-1}^{\dagger} \\ \dot{\tilde{K}}_{0} & \sqrt{t} \mathbb{I}_{d_{2}} & 0 & \ldots & 0 \\ \dot{\tilde{K}}_{1} & 0 & \sqrt{t} \mathbb{I}_{d_{2}} & \ldots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ \dot{\tilde{K}}_{k-1} & 0 & 0 & \ldots & \sqrt{t} \mathbb{I}_{d_{2}} \end{array}\right), $$ where $\dot{K_i}^\dagger$ stands for a matrix and the dot stands for derivative respect to a parameter inside the matrix.
My question is why the requirement of the positive semi-definite of the matrix $A$ is equivalent to the condition: $$ \alpha_{\tilde{K}}=\sum_{i} \dot{\tilde{K}}_{i}^{\dagger} \dot{\tilde{K}}_{i} \leq t \mathbb{I}_{d_{1}}. $$ Thanks a lot!