Doruk's Linear Algebra Calculator

Features

• 🔢 Comprehensive Calculators: Vectors, matrices, systems of linear equations, and series/summations.
• 📐 3D Geometry Operations: Planes, lines, intersections, and distance calculations in 3D space.
• 🧮 Batch Matrix Operations: Automatically evaluate multiple matrix expressions from exercise lists.
• 🔍 Linear Mapping Analysis: Test if mappings are linear and generate matrix representations.
• 📊 Series & Pattern Recognition: Analyze sequences, calculate geometric/arithmetic series, and solve summation exercises.
• 🎨 Interactive Visualizations: Understand concepts with dynamic graphical representations and LaTeX formatting.
• 📚 Step-by-Step Explanations: Detailed walkthroughs with mathematical formulas and solution steps.
• 🧠 Practice & Learn: Interactive quizzes and comprehensive learning resources.
• 🌐 Modern Web Interface: Beautiful, responsive design with search functionality and organized categories.

A comprehensive toolkit for learning and solving linear algebra problems, built as a modern web application with Streamlit.

Quick Start

# Clone the repository
git clone https://github.com/peaktwilight/linear-algebra-calculator.git
cd linear-algebra-calculator

# Install dependencies
pip install -r requirements.txt

# Run the web application
streamlit run streamlit_app.py

Available Operations

🔢 Vector Operations

• Vector Normalization, Projection, Angle Calculation
• Cross Product, Triangle Area, Point-Line Distance
• Collinearity Checking

📐 Lines and Planes

• Plane from 3 Points - Calculate plane equation from three non-collinear points
• Point-to-Plane Distance - Find shortest distance from point to plane
• Line-Plane Intersection - Calculate where lines intersect planes in 3D
• Plane Equation Converter - Convert between coordinate, vector, and parametric forms

📊 Matrix Operations

• Matrix Addition, Subtraction, Multiplication, Transpose
• Determinant, Inverse, Eigenvalues & Eigenvectors
• Batch Expression Calculator - Automatically solve multiple matrix expressions

⚖️ Systems of Linear Equations

• Gaussian Elimination, Row Operations Analysis
• Null Space Calculation, Free Parameter Analysis
• Vector Solution Checking, Geometric Interpretation

📈 Series & Summations

• Geometric and Arithmetic Series Calculation
• Pattern Recognition in Sequences
• Summation Exercise Solver with step-by-step solutions

🔍 Linear Mappings

• Linearity Testing for Various Function Types
• Matrix Representation Generation

File Structure

• streamlit_app.py: Main web application entry point
• st_components/: Streamlit interface components
  • st_math_utils.py: Core mathematical utilities and functions
  • st_calculator_operations.py: Main calculator operations
  • st_batch_calculator.py: Batch matrix expression evaluator
  • st_summation_calculator.py: Series and summation calculator
  • st_quiz_ui.py: Interactive quiz interface
  • st_learning_resources.py: Educational content and tutorials
  • Various operation mixins for specialized functionality
• given_reference/: Core algorithms and reference implementations
• requirements.txt: Python dependencies
• CLAUDE.md: Development notes and configuration

Online Version

A hosted version of the web interface is available at: lag.doruk.ch

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© 2025 Doruk | FHNW Linear Algebra Module