7.6-06 Column-stochastic matrices

Column-stochastic matrices

Construct and use transition matrices with one consistent column-vector convention. Interpret individual entries, preserve probability mass, compose updates in the correct order and recognize absorbing states.

What you will practise

• Build destination columns
• Check stochastic constraints
• Compute one-step distributions
• Compose transition matrices

Prerequisites and study approach

This microlearning belongs to Module 7, Eigenvalues and Dynamical Systems, in the Complete Linear Algebra Course. Before starting, review probability vectors and matrix multiplication. The questions move from recognition and short calculations to connected reasoning. Single-select questions require one answer; multiselect questions ask you to evaluate every statement independently.

The final example tracks remaining probability at a transient state next to an absorbing state. Work out your own result before checking the choices, then use the explanation to compare the reasoning and diagnose a mistaken assumption. This focused practice connects conceptual understanding with reliable problem solving and supports review before the next microlearning.