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Singular vs Non-Singular Matrix Visualizer

Run the Singular Matrix Visualizer Fullscreen

Edit the MicroSim with the p5.js editor

About This MicroSim

This visualization shows the fundamental geometric difference between singular and non-singular matrices.

Key Insights:

  • Non-singular (det ≠ 0): Transformation is reversible, area preserved (scaled)
  • Singular (det = 0): Transformation collapses dimension, not reversible

Watch how the unit square transforms:

  • Green: Non-singular, positive determinant (orientation preserved)
  • Purple: Non-singular, negative determinant (orientation flipped)
  • Red line: Singular - the square collapses to a line!

How to Use

  1. Click preset buttons: Singular, Non-singular, or Random matrix
  2. Use morph slider: Smoothly animate from identity to target matrix
  3. Toggle grid: Show/hide the transformed coordinate grid
  4. Watch the collapse: See how singular matrices flatten the plane

Embedding

1
<iframe src="https://dmccreary.github.io/linear-algebra/sims/singular-matrix/main.html" height="482px" scrolling="no"></iframe>

Lesson Plan

Learning Objectives

Students will be able to:

  1. Recognize singular matrices visually and algebraically
  2. Explain why singular matrices are not invertible
  3. Connect det = 0 to dimension collapse

Suggested Activities

  1. Morph slowly: Watch the exact moment area becomes zero
  2. Column relationship: When singular, what's the relationship between columns?
  3. Predict singularity: Before clicking, guess if a random matrix will be singular

Assessment Questions

  1. Why can't you "undo" a singular transformation?
  2. What happens to a circle under a singular transformation?
  3. If two columns are parallel, what is the determinant? Why?

References