This section introduces a video that demonstrates the convergence of a stochastic matrix to its steady state. The video was created using the Manim library and shows the powers of a stochastic matrix converging to a limit.

The video shows the following:

1. The initial stochastic matrix, \(P\).
2. The powers of the matrix, \(P^2\), \(P^3\), and so on.
3. The convergence of the matrix to a steady state, where all the rows are the same.

The values in the matrix are color-coded to show their value between 0 and 1. White represents 0 and blue represents 1.

This video was produced using a combination of Gemini CLI, Manim, and the MCP server (manim-server).