About Linear Algebra

This section introduces Linear Algebra, one of the most powerful and widely used branches of mathematics. You’ll learn how to work with vectors and matrices, solve systems of equations, understand transformations, and see why this subject is fundamental to computer graphics, machine learning, physics, engineering, and game development.

Linear Algebra is the study of linear relationships - relationships that can be represented as straight lines, planes, or higher-dimensional flat spaces.

Instead of dealing with curves and nonlinear equations (like in Calculus), linear algebra focuses on things that scale proportionally:

• Vectors (directions and magnitudes)
• Matrices (grids of numbers that represent transformations)
• Systems of linear equations
• Vector spaces and linear transformations

Linear Algebra is everywhere:

• Game Development: 3D transformations, camera systems, animations, physics engines
• Computer Graphics: Rotating, scaling, and projecting objects on screen
• Machine Learning: Neural networks are built on matrices and linear transformations
• Physics and Engineering: Solving systems with many variables, quantum mechanics
• Data Science: Principal Component Analysis (PCA), least squares fitting

Many people say Linear Algebra is the “language of modern technology.”

In this section we’ll build from the fundamentals up:

1. Vectors and Vector Operations
2. Matrices and Matrix Operations
3. Systems of Linear Equations
4. Determinants and Inverses
5. Vector Spaces and Linear Independence
6. Eigenvalues and Eigenvectors
7. Linear Transformations
8. Applications in Graphics and Games

We’ll keep the same supportive, practical tone as the rest of the site - with plenty of real-world examples (especially game development and 3D math).

Think of Linear Algebra as the toolkit that lets you manipulate space itself. Once you understand vectors and matrices, you’ll suddenly see how 3D games rotate characters, how AI models process data, and how physicists describe forces and motion.

You’re building on everything you learned in Calculus. Now we’re moving from rates of change to structure and transformation.