An Interactive Visual Journey Through Linear Algebra

This tool helps you understand linear algebra concepts through interactive 3D visualizations.

Lessons:

• Vectors in 3D: Understand vectors as directed quantities in space
• Vector Addition: See how vectors combine using the parallelogram rule
• Dot Product: Visualize projection and angles between vectors
• Cross Product: Discover perpendicular vectors and area
• Matrix Transformations: Watch how matrices transform space
• Eigenvalues: Find special vectors that only scale
• Basis Vectors: Build any vector from fundamental directions
• Determinant: See how transformations scale area/volume

Controls:

• Left Mouse: Rotate the view
• Right Mouse: Pan the camera
• Scroll: Zoom in/out
• Sliders: Adjust vector components or matrix values
• Play Button: Animate transformations (where available)

Tips:

• Experiment with extreme values to build intuition
• Watch how the coordinate grid transforms
• Pay attention to the mathematical formulas
• Try to predict what will happen before adjusting