7.6-05 Phase portraits

Phase portraits

Classify planar discrete phase portraits from their eigenstructure. Identify sinks, sources, saddles and spirals, then compare the discrete interpretation with the continuous model using the same matrix.

What you will practise

• Classify contracting and expanding modes
• Find stable directions of saddles
• Interpret turning and sign reversal
• State which time convention is used

Prerequisites and study approach

This microlearning belongs to Module 7, Eigenvalues and Dynamical Systems, in the Complete Linear Algebra Course. Before starting, review discrete eigenmode evolution and complex conjugate pairs. 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 question determines the exact set of initial states approaching a saddle rather than classifying every trajectory identically. 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.