Positive Semi Definite
PSD differential equation
Any matrix $A_{d \times d}$ is said to be PSD if $x^TAx \geq$ 0 $\forall$ vector $x_{d \times 1}$.
Examples Identity matrix $I_{d \times d}$: $$ A = \begin{bmatrix} 1 & 0 & 0 & 0 \newline 0 & 1 & 0 & 0 \newline 0 & 0 & 1 & 0 \newline 0 & 0 & 0 & 1 \end{bmatrix} $$
Then
\begin{align} x^TAx &= \sum_{i = 1}^d \sum_{i = 1}^d A_{i,j}x_ix_j \newline &= \sum_{i = 1}^d A_{i,i} x_i^2\newline &= \sum_{i = 1}^d x_i^2 \newline &\geq 0 \end{align}……