Fun fact, not mentioned in the video:If the matrix A is singular, then the process is losing information because two linearly independent vectors in the input space could be mapped to the same output vector, making them indistinguishable. When the professor discussed the matrix for ordinary differentiation of a polynomial function, notice that it was singular. This corresponds to the arbitrary constant of integration i.e. information will be lost, so you save it ahead of time via initial conditions so you can reconstruct the input vector.Linear algebra is amazing for this kind of insight.####[]