 State-transition matrix

A state-transition matrix, often denoted as \( \mathbf{T} \) or \( \Phi(t) \), is used in the context of dynamic systems, particularly in the study of linear time-invariant (LTI) systems, control theory, and state-space representations of systems. It provides a way to describe how the state of a system evolves over time in response to inputs and initial conditions.