Topic: Applications of Diagonalization

Why the Eigenmode Formula Holds

The Fibonacci Sequence from Its Companion Matrix

Stationary Distributions as Eigenvectors

State-Space Models for Discrete-Time Linear Systems

Recurrence Relations as Matrix Dynamics

Population Growth from Projection Matrices

Perron-Frobenius for Positive Two-by-Two Matrices

Markov Transition Matrices and Probability-State Conventions

Exact Iteration of Two-State Markov Chains

Eigenvalue Magnitudes and Long-Term System Behavior