Matrix Powers Explained: Unlocking the Secrets of Diagonalization and Steady States

In this video, we explore matrix diagonalization and why it simplifies raising matrices to higher powers. Using an example of population movement, we uncover how repeated multiplication reveals steady states—long-term patterns in dynamic systems. Watch as we break down diagonalization step by step, making complex calculations simple and practical. 00:00 – Introduction - what is diagonalization, and how does it help us 01:15 – Why we raise matrices to higher powers - population movement model (steady state) 12:12 – Derivation of diagonalization formula 20:16 – Simple example