Definition (Observability matrix)

For the LTIC system $$\begin{cases} \dot{x}(t)=Ax(t)+Bu(t) \\ y(t)=Cx(t)+Du(t) \end{cases}$$we define the observability matrix as $$\mathcal{O}^{\top}_{CA}=\begin{bmatrix}C \\ CA \\ \ddots \\ CA^{n-1} \end{bmatrix}$$