The document discusses linear dynamical systems and controllability of linear systems. It defines dynamical systems as mathematical models describing the temporal evolution of a system. Linear dynamical systems are ones where the evaluation functions are linear. Controllability refers to the ability to steer a system from any initial state to any final state using input controls. The document provides the definition of controllability for linear time-variant systems using the controllability Gramian matrix. It also gives the formula for the minimum-norm control input that can steer the system between any two states. An example of checking controllability for a time-invariant linear system is presented.