Interactive Linear Algebra Visualizer

An interactive Python script that allows you to visualize linear algebra concepts in 2D and 3D space with custom input values.

Features

2D Visualizations (2 Variables)

1. Vectors: Vector addition and subtraction with parallelogram visualization
2. Linear Equation: Single line (ax + by = c)
3. System of Linear Equations: Two lines with intersection point solution
4. Linear Transformation: Apply 2x2 matrices to vectors

3D Visualizations (3 Variables)

1. Vectors: Vector addition and cross product
2. Plane: Single plane with normal vector (ax + by + cz = d)
3. System of Planes: Intersection of two planes
4. Linear Transformation: Apply 3x3 matrices to vectors

Installation

1. Install the required dependencies:

pip install -r requirements.txt

Usage

Run the script:

python main.py

Interactive Menu

The program will guide you through:

1. Choose dimension: Select 2D (2 variables) or 3D (3 variables)
2. Choose visualization type: Pick from vectors, equations/planes, or transformations
3. Enter your values: Input coefficients, constants, or vector components
4. View the plot: The visualization will be displayed
5. Modify or save: You can:
   • Modify values and refresh the diagram
   • Save the current plot as a PNG image
   • Return to the main menu

Example Usage

2D Linear Equation Example:

Choose: 2 Variables (2D)
Choose: Linear Equation
Enter a: 2
Enter b: 3
Enter c: 6

This will plot the line 2x + 3y = 6

3D Vector Example:

Choose: 3 Variables (3D)
Choose: Vectors
Enter v1: (1, 0, 0)
Enter v2: (0, 1, 0)

This will show vector addition and cross product

System of Equations Example:

Choose: 2 Variables (2D)
Choose: System of Linear Equations
Equation 1: 2x + y = 5
Equation 2: x - y = 1

This will show both lines and their intersection point (2, 1)

Features

• Real-time visualization with custom inputs
• Ability to modify values and refresh plots
• Save visualizations as high-resolution PNG images
• Automatic solution calculation for systems of equations
• Additional information (determinants, dot products, cross products)
• Error handling for invalid inputs

Requirements

• Python 3.7+
• NumPy
• Matplotlib

Tips

• For linear equations, coefficients can be positive or negative
• For transformations, try identity matrix [[1,0],[0,1]] first to see basis vectors
• The plot automatically scales to fit your data
• You can rotate 3D plots by clicking and dragging