How cayley hamilton theorem is used in practical life?

The Cayley-Hamilton Theorem states that every square matrix satisfies its own characteristic polynomial. In practical applications, this theorem is used in various fields such as control theory and systems engineering, where it helps in system stability analysis and in solving differential equations. It also facilitates computational techniques in computer graphics, robotics, and structural engineering by simplifying matrix computations, enabling efficient algorithms for simulations and optimizations. Additionally, it aids in finding matrix inverses and exponentials, which are crucial in numerous engineering applications.