What is Linear Algebra?

Linear algebra studies vectors, vector spaces, linear transformations, and systems of linear equations. It's foundational for computer graphics, machine learning, physics, and engineering.

Vectors

Vectors represent quantities with both magnitude and direction. In 2D, a vector v = (x, y). Vectors can be added, scaled, and used to represent forces, velocities, and positions.

Matrices

Matrices are rectangular arrays of numbers. They represent linear transformations and systems of equations. Matrix multiplication combines transformations, and matrix inversion solves systems.

Applications

Linear algebra powers computer graphics (3D transformations), machine learning (neural networks), physics (quantum mechanics), engineering (structural analysis), and data science (principal component analysis).