Matrices

State Transition Matrices

What and why?

By computing transition matrices, we are able to see how a system will progress over time. If the vector happens to be an eigenvector of the matrix, then we'll be able to compute the steady state vector (aka as time approaches infinity, what the vector will be).

Incidence Matrices

What and why

Incidence matrices or edge-node matrices are a way to express a relationship between two nodes. Unlike transition matrices, incidence matrices only show a relationship ($0$ for no relationship and $1$ for a relationship) rather than the actual relationship indicating the proportion of flow. This type of matrix will be useful in the upcoming unit on circuits. It will help us represent Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL).