Linear algebra is a foundational branch of mathematics with widespread applications across disciplines. Here are key areas where it plays a critical role:
💻 1. Computer Graphics & Vision
- 3D Modeling: Matrices transform vertices to create realistic animations
- Image Compression: Singular Value Decomposition (SVD) reduces file sizes
- Robotics: Linear transformations enable motion planning
🤖 2. Machine Learning
- Feature Space: Vectors represent data points in high-dimensional space
- Neural Networks: Weight matrices process information through layers
- Principal Component Analysis (PCA): Orthogonal projections for dimensionality reduction
🧪 3. Physics & Engineering
- Quantum Mechanics: State vectors and operators describe particles
- Structural Analysis: Systems of equations model forces in architecture
- Electrical Circuits: Matrix methods solve for currents in complex networks
📊 4. Economics & Social Sciences
- Input-Output Models: Matrices analyze economic interdependencies
- Game Theory: Linear equations solve for equilibrium strategies
- Population Dynamics: Systems model growth patterns in ecology
For deeper exploration, visit our Linear Algebra Overview section.