9. Linear Algebra

Linear algebra is a fundamental part of scientific computing, forming the language used to describe everything from machine learning models and quantum mechanics to economic systems and 3D graphics. Julia is a premier language for these tasks, combining an intuitive, math-friendly syntax with exceptional performance.

This chapter introduces Julia’s powerful LinearAlgebra package. We’ll cover the essentials of creating and manipulating vectors and matrices, solving complex systems of equations, and performing key analyses like eigendecomposition. We’ll also show another of Julia’s strengths: its ability to leverage special matrix structures to write code that is not only correct but also fast and memory-efficient.